I must admit that I usually find videos that have a catch phrase at the end super annoying. That said, whenever something cool happens in my life I now find myself saying “how exciting!” So well played sir! Keep up the great work. ❤
Was not expecting to hop onto youtube today and learn more math from a stereotypical looking college frat bro in under 4 minutes than I did all semester in my calculus class, but very informative!
Look, I like to dunk on how unhelpful maths classes sometimes are, but this is literally just familiar triangles, pythagorean theorem and simple arythmatic. Any 15 year old with a B in maths should solve this in 5 minutes tops.
Nope. You're the one making yourself smart by trying to solve the problem. He's just there to help when you give up, succeed or fail. Respect to the guy obviously, his presentation is great.
1:50 The way I would've done it from here is this: Make b = 4a -13 Plug in: a + 4(4a - 13) = 4a 16a + a - 52 = 4a 17a - 4a = 52 13a = 52 a = 4 Plug in a = 4 for the equation for b 4(4) - 13 = b 16 - 13 = b 3 = b Solve for the smallest triangles hypotenuse (3^2 + 4^2 = c^2) The smallest triangle is a 3 4 5 triangle (special right triangle), so c = 5 Solve for the squares 5 * 5 = 25 Since there's 4 squares: 25 * 4 = 100 That's our answer, I'm not sure if my way takes any longer, I just don't like dealing with fractions at all
Idk anything about math, in fact I've stop doing math at 15, but I really enjoyed learning this topic back in school, now I'm completly washed up ofc. But god, I love this channel !
I'm not sure if this is just the perspective of Andy's camera or the room or if he is tall, but it looks like he is about to hit the ceiling, no? If this is some secret joke to make it seem he is 9ft tall that'd be amazing. That was another fun problem, I adore your enthusiasm, and humour, its good fun! So good on ya my man! Have a nice day! :)
Solving this before watching the video. So, the square on the bottom combined with the angles on either side of it on the bottom line is 180 degrees. The square has a 90-degree angle which is translated to the two 90-degree angles on the bottom edges of the large square. The angles on the sides of the bottom square also translate to the opposite angles of the two triangles on either side of the shaded area, showing that the triangles are the same, just differently scaled. The hypotenuse of both triangles also matches up with the shaded area, with the smaller triangle being the same as the side of one square, while the larger triangle matches with the side of all four squares. Labeling the sides of the triangle similar to the Pythagorean theorem (a^2+b^2=c^2), the side of the square is c, while the rectangle made up of four squares is 4c. This also shows that the larger triangle is 4x as big as the smaller one, so we'll also label the longer ends a and 4a, and the shorter ends b and 4b. This then shows that the sides of the large square are equal to 4a, 4b+a, and 13+b. So, if we start with 4b+a=13+b and subtract 4b from both sides, we get that a=13-3b. Multiply both sides by 4 and you get 4a=52-12b. Now, since 4a also = 13+b, we can say 13+b=52-12b. subtract 13 from both sides and add 12b to both sides and you wind up with 13b=39. Then you divide both sides by 13 to get b=3. Plug that back into 4a=13+b to get 4a=13+3 or 4a=16. Divide both sides by 4 to get a=4. Now, by using the Pythagorean theorem, we can determine that these are 3, 4, 5 right triangles, meaning that c=5 (a^2+b^2=c^2, 3^2+4^2=c^2, 9+16=c^2, 25=c^2, c=5) Now, the area of the small square is the square of the side, being 25. Multiply that by four squares, and you get the total area of the shaded rectangle to be 100. (conversely, you could multiply the side by 4 to get 20 for the long leg of the rectangle, and then multiply that by the shorter side of 5, to get the area of 100 as well)
Nice. My solve was similar, but I labeled the shorter leg a and longer leg b, and I multiplied by 4 rather than dividing by 4 and avoided having to use any fractions.
0:57 you missed one piece of information (but obviously it didn’t make much of a difference), the side length of blue-green on the larger triangle has a length of 13 + b of the smaller triangle.
@@kaitek666imgur.com/a/AxMbvaH Here's the image and how I labelled it. So I started by proving congruent triangles the same way. △ABC ᔕ △A'BC', therefore, AB/A'B = BC/BC' (x-13)/sqrt(16y^2-x^2) = y/4y = 1/4 4(x-13) = sqrt(16y^2 - x^2) (*) We have: x = AC + CA' = sqrt(y^2 - (x-13)^2) + sqrt(16y^2 - x^2) Substitution with (*) we get: x = sqrt(y^2 - (16y^2 - x^2)/16) + 4(x - 13) x = sqrt(x^2/16) +4x -52 3x + x/4 = 52 -> x = 16 -> y = 5 -> Area of shaded area = 4y^2 = 100 (sq units) Hope this helps!
@@SiddharthHarsh yar Mera abhi sirf civics hua hai, economics aadha ho gaya aaj kar lunga. Kal history pura + geography thoda aur parso geography khatam kar dunga. Fir 1 sample paper dunga Digraj sir ka
I neglected to use the ratio 1:40 of the sides, so I went straight into trigonometric ratios... and solved it, but in a slightly harder way, but without Pythagoras.
Yeah. The few times I've been punished for assuming a figure is to scale unless stated otherwise just won't let any geometrical intuition rest well within me 😂
Solution: First, lets give some names: S = short leg of lower left triangle L = long leg of lower left triangle X = small square sidelength and hypotenuse of the lower left triangle The bottom left and right triangles are similar due to identical angles. We also know, that the bigger one is 4 times the smaller one, as the hypotenuses are 4X and X repectively. Therefore we know, that the big square has the side length of 4L OR 4S + L. As such, we have: 4L = 4S + L |-L 3L = 4S So the big triangle has the legs 3L and 4L. This is just a multiple of the pythagorean triple 3-4-5. As such, the hypotenuse is 5L, so 5L = 4X. Last but not least, we know that 4L = S + 13. This is everything we need to find X: 4L = S + 13 4(4S/3) = S + 13 |*3 16S = 3S + 39 |-3S 13S = 39 |/13 S = 3 4X = 5L 4X = 5 * (4S/3) 4X = 5 * (4*3/3) 4X = 5 * 4 |/4 X = 5 The shaded area is 4x² = 4 * 5² = 4 * 25 = 100 units²
awesome question, and well-solved and explained. i thought they asked for the shaded area that is within the square spoilers: . . . . . . . . . . . . . . . . . it's 725/8, if anyone cares
There are math channels on RUclips, which make from a simple x-equation a 5 minute video clip. Bummer. And your stuff? I'm not the dumbest in using math, but when i see one of your problems, i usually go: huh? what? HOW? And then you solve it in 3-4 minutes, using just simple algebra and geometry. Awesome!
Yeah so I had a way worse way of solving it and I still can't confirm if it works because I tried it on the calculator twice and it failed :) Anyway, I used the two similar triangles that you used but then decided that I would call the side of the big square x and write the side of a red square in terms of x by using the small triangle in the bottom left corner. I then created a new triangle by connecting the point the shaded area intersects on the left side and the top right corner. That triangle would have the sides x, 13, and sqrt((85x^2)/16-130x+845) If it's already wrong at this point or if I messed something up beyond that I do not know but tl;dr my method could probably work but it's too messy and I'm too lazy to figure out what the problem is
The shaded part that sticks out at the top is also one of those similar triangles, right angle pointing up this time. You know that one side of that triangle is 5 and you also know that another side is 3/4 times 5. Both these sides are next to the right angle so you just multiply them with each other and divide by 2 to get the area of that triangle. 5*(3/4)*5 =5*(15/4) =75/4 (75/4)/2=75/8 Then subtract that from 100 (the whole shaded area). 100-(75/8) =(800/8)-(75/8) =725/8
In middle Egypt they knew "the area of a square of 100 is equal to that of two smaller squares. The side of one is ½ + ¼ the side of the other." I thought it interesting the shaded areas is 100 and you got b=3/4a on your working
So, knowing this here's another way of solving once you know the scale factor is 4 and have worked out the bottom left triangle: You know the length given is 13, you also know the small triangle at the bottom left hand corner is 3,4,5. So the length of the side of the black square is 16. So because we now know the length is 16, that means the side opposite it is also 16. So 3/4 of 16 is 12 which means the other side of the triangle is length 12. 12^2 plus 16^2 is 400. Divide 400 by 4(the scale factor) and you get 100. because 3,4,5 is also equivalent to 6,8,10 and therefore 12,16,20 then you now know the hypotenuse of the triangle on the right is 20 and the hypotenuse can be divide into 4 lengths, 20/4 is 5 which gives you the hypotenuse of the bottom left triangle and then you get the areas of 25 for one square. Then you go 25*4 which is 100. which proves the Egyptians were right about a side being 3/4 the length of another
when i see a colorful handmade drawing, i can instantly see that is a Catriona Agg question.. bc nobody redraw the question digitally .. dont know why tho :))))
Would it be 96.625. By using the same method the top left triangle is also similar and we can do the area of the square minus the area of all of the triangles.
There's a special spot in heaven for anyone who creates mathematical problems where the answer is 0, 1, 10, or 100
😂
For people who make the answer a whole number
Nah just making it an integer is good enough
Sounds like a fake spot
and those with pi as well
Me seeing my homework: "This looks important, let's put a box around it"
I do this at work as well, in several different colors actually.
The problem with that is you cannot tell the teacher that your dog ate it!
Proceeds to put the notebook in a box.
Life would be so much simpler if we could put a box around things that look important.
you can
@@vexinum3837 how do you put a box around things that are important in life?
@@Walkingthrough1 you put a box around them.
@sinrj9028 how do you put a box around your thoughts
@@KenjiLaurvick wear a box as a helmet
Once again, I over-complicated my approach and had to abandon my work. Then I watched your thought process. How exciting.
I want this man's ability to breakdown things
didnt even thought about checking angles
wow
think*
You will get it with time, if you keep practicing.
Well, the similarity thing was the first one I noticed. Bet he found out from comparing the angles. Just observe everything.
One day..I’ll solve the problem before watching the video
Do it now.. no tomorrow comes
Me too brother me too
Skill issue
hahaha 😂
Bro one day, or day one
*Andy receiving his Nobel Prize* “That looks important, let’s put a box around it.”
Love you Andy
I must admit that I usually find videos that have a catch phrase at the end super annoying. That said, whenever something cool happens in my life I now find myself saying “how exciting!” So well played sir! Keep up the great work. ❤
Bro I love watching math problems from you they’re so satisfying, how exciting.
Was not expecting to hop onto youtube today and learn more math from a stereotypical looking college frat bro in under 4 minutes than I did all semester in my calculus class, but very informative!
Look, I like to dunk on how unhelpful maths classes sometimes are, but this is literally just familiar triangles, pythagorean theorem and simple arythmatic. Any 15 year old with a B in maths should solve this in 5 minutes tops.
I respect this man, he is single-handedly, making us smarter if we pay attention!
Cheers b 🤙🏽
Every teacher ever: "am I a joke to you?"
Nope. You're the one making yourself smart by trying to solve the problem. He's just there to help when you give up, succeed or fail.
Respect to the guy obviously, his presentation is great.
If my teachers had taught me as you explain, I would have loved mathematics more than I do.
Frrrrrrrrr
It feels amazing to be able to solve it in the same time as you even tho my last maths class was almost 5 years ago
With just a 13, bro was about to calculate the mass of the sun 💀
💀
1:50 The way I would've done it from here is this:
Make b = 4a -13
Plug in: a + 4(4a - 13) = 4a
16a + a - 52 = 4a
17a - 4a = 52
13a = 52
a = 4
Plug in a = 4 for the equation for b
4(4) - 13 = b
16 - 13 = b
3 = b
Solve for the smallest triangles hypotenuse (3^2 + 4^2 = c^2)
The smallest triangle is a 3 4 5 triangle (special right triangle), so c = 5
Solve for the squares
5 * 5 = 25
Since there's 4 squares: 25 * 4 = 100
That's our answer, I'm not sure if my way takes any longer, I just don't like dealing with fractions at all
This guy making the world a better place
Idk anything about math, in fact I've stop doing math at 15, but I really enjoyed learning this topic back in school, now I'm completly washed up ofc. But god, I love this channel !
This is absolutely brilliant. You are my hero.
I'm not sure if this is just the perspective of Andy's camera or the room or if he is tall, but it looks like he is about to hit the ceiling, no? If this is some secret joke to make it seem he is 9ft tall that'd be amazing.
That was another fun problem, I adore your enthusiasm, and humour, its good fun! So good on ya my man! Have a nice day! :)
Haha just noticed, it's probably bcuz of the camera pov ig
I like it gives a distance of 13 and you completely ignore it and still solve it.
Maths has never been so reasonable before 🤩
One thing I learned is if it looks important, put a box around it.
Thank you. You are very skilled and would be nervous playing board games with you.
Solving this before watching the video. So, the square on the bottom combined with the angles on either side of it on the bottom line is 180 degrees. The square has a 90-degree angle which is translated to the two 90-degree angles on the bottom edges of the large square. The angles on the sides of the bottom square also translate to the opposite angles of the two triangles on either side of the shaded area, showing that the triangles are the same, just differently scaled. The hypotenuse of both triangles also matches up with the shaded area, with the smaller triangle being the same as the side of one square, while the larger triangle matches with the side of all four squares. Labeling the sides of the triangle similar to the Pythagorean theorem (a^2+b^2=c^2), the side of the square is c, while the rectangle made up of four squares is 4c. This also shows that the larger triangle is 4x as big as the smaller one, so we'll also label the longer ends a and 4a, and the shorter ends b and 4b. This then shows that the sides of the large square are equal to 4a, 4b+a, and 13+b. So, if we start with 4b+a=13+b and subtract 4b from both sides, we get that a=13-3b. Multiply both sides by 4 and you get 4a=52-12b. Now, since 4a also = 13+b, we can say 13+b=52-12b. subtract 13 from both sides and add 12b to both sides and you wind up with 13b=39. Then you divide both sides by 13 to get b=3. Plug that back into 4a=13+b to get 4a=13+3 or 4a=16. Divide both sides by 4 to get a=4. Now, by using the Pythagorean theorem, we can determine that these are 3, 4, 5 right triangles, meaning that c=5 (a^2+b^2=c^2, 3^2+4^2=c^2, 9+16=c^2, 25=c^2, c=5) Now, the area of the small square is the square of the side, being 25. Multiply that by four squares, and you get the total area of the shaded rectangle to be 100. (conversely, you could multiply the side by 4 to get 20 for the long leg of the rectangle, and then multiply that by the shorter side of 5, to get the area of 100 as well)
Nice. My solve was similar, but I labeled the shorter leg a and longer leg b, and I multiplied by 4 rather than dividing by 4 and avoided having to use any fractions.
Same
0:57 you missed one piece of information (but obviously it didn’t make much of a difference), the side length of blue-green on the larger triangle has a length of 13 + b of the smaller triangle.
1:43
@@Chrisratata I know, my point is that he didn’t establish that earlier, implying that the information was not available yet, even though it was.
I LOVE the lets put a box around it
As soon as I looked at it I knew there were going to be some similar triangles and then I thought "how... exciting"
As a Brit I appreciate the way you pronounce little 👌
i solved it in a different way but got to the same answer, feels nice
do you remember what you did? can you tell us?
@@kaitek666imgur.com/a/AxMbvaH Here's the image and how I labelled it.
So I started by proving congruent triangles the same way.
△ABC ᔕ △A'BC', therefore, AB/A'B = BC/BC'
(x-13)/sqrt(16y^2-x^2) = y/4y = 1/4
4(x-13) = sqrt(16y^2 - x^2) (*)
We have: x = AC + CA' = sqrt(y^2 - (x-13)^2) + sqrt(16y^2 - x^2)
Substitution with (*) we get:
x = sqrt(y^2 - (16y^2 - x^2)/16) + 4(x - 13)
x = sqrt(x^2/16) +4x -52
3x + x/4 = 52
-> x = 16
-> y = 5
-> Area of shaded area = 4y^2 = 100 (sq units)
Hope this helps!
I'd like to see Andy solving these real-time
Love this one. How exciting
I loved the part where he said a bunch of crazy and unexpected logic that actually made sense (basically the whole video) lol
My exams are coming, and i am watching this for no reason
Yes
SST? Kitni taiyari hogyi?
@@Rohanbeingbusy 😂😂 divided by distance ,United by boards
@@aalekhjain2682 economics aur geography complete ho gaya hai history aur civics ke liya digraj sir ka notes hai 😅
@@SiddharthHarsh yar Mera abhi sirf civics hua hai, economics aadha ho gaya aaj kar lunga. Kal history pura + geography thoda aur parso geography khatam kar dunga. Fir 1 sample paper dunga Digraj sir ka
My good sir, I walk through a world in which "fun" and "math" are impossible to fit in the same sentence.
I neglected to use the ratio 1:40 of the sides, so I went straight into trigonometric ratios... and solved it, but in a slightly harder way, but without Pythagoras.
I had a gut feeling it was gonna be a 3,4,5 triangle. The proportions are just so recognizable
Yeah. The few times I've been punished for assuming a figure is to scale unless stated otherwise just won't let any geometrical intuition rest well within me 😂
@@Lillmackish i mean yeah, you've still gotta confirm it lol
Solution:
First, lets give some names:
S = short leg of lower left triangle
L = long leg of lower left triangle
X = small square sidelength and hypotenuse of the lower left triangle
The bottom left and right triangles are similar due to identical angles.
We also know, that the bigger one is 4 times the smaller one, as the hypotenuses are 4X and X repectively.
Therefore we know, that the big square has the side length of 4L OR 4S + L.
As such, we have:
4L = 4S + L |-L
3L = 4S
So the big triangle has the legs 3L and 4L. This is just a multiple of the pythagorean triple 3-4-5.
As such, the hypotenuse is 5L, so 5L = 4X.
Last but not least, we know that 4L = S + 13.
This is everything we need to find X:
4L = S + 13
4(4S/3) = S + 13 |*3
16S = 3S + 39 |-3S
13S = 39 |/13
S = 3
4X = 5L
4X = 5 * (4S/3)
4X = 5 * (4*3/3)
4X = 5 * 4 |/4
X = 5
The shaded area is 4x² = 4 * 5² = 4 * 25 = 100 units²
awesome question, and well-solved and explained.
i thought they asked for the shaded area that is within the square
spoilers:
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it's 725/8, if anyone cares
Good work Mr. Math. One more problem down
Ok but that fact about the Pythagorean Triple triangle was just showing off.
how
4b+a=13 +b> a=13-3b
4b+a=4a > 4b=3a
4b=69-9b
B=3
A=4
C=5
Area=100
This channel looks important, Let’s put a sub around it. How exciting.
1:05 “let’s change the 4 c’s into 4c”
I'm so glad cad programs exist 😂
... brilliant as always ...
someone should put a box around you because your important!
This title is already a paradox in itself!
That feeling when you solve it before watching the video...
I think we need more information like how those those triangles are the same
Solved before watching! I love when the answer is magically exactly 100
There are math channels on RUclips, which make from a simple x-equation a 5 minute video clip. Bummer. And your stuff? I'm not the dumbest in using math, but when i see one of your problems, i usually go: huh? what? HOW? And then you solve it in 3-4 minutes, using just simple algebra and geometry. Awesome!
Yeah so I had a way worse way of solving it and I still can't confirm if it works because I tried it on the calculator twice and it failed :)
Anyway, I used the two similar triangles that you used but then decided that I would call the side of the big square x and write the side of a red square in terms of x by using the small triangle in the bottom left corner. I then created a new triangle by connecting the point the shaded area intersects on the left side and the top right corner. That triangle would have the sides x, 13, and sqrt((85x^2)/16-130x+845)
If it's already wrong at this point or if I messed something up beyond that I do not know but tl;dr my method could probably work but it's too messy and I'm too lazy to figure out what the problem is
The evil I tetris piece is messing with my perfect square, Calculate his area to bombard it
What software do you use for the animations?
Beautiful.
similar triangles were hell...
So, the area of the red squares in the big square is 90.625! Fun!
i thought we were solving for the area of the shaded squares inside the black box
is there a way to solve it if the problem is "What is the area of the shaded region within the black box?"
Nice!
the 13 skipped entirely, nice
13 was needed to solve the problem, otherwise it was impossible
oh yea missed that nice
ahhh i wish i can get good at solving those problems because they are so fun! only problem is i'm bad at maths :(
Good job.
amazing!
How exciting!
I thought It was asking for the shaded area enclosed in the box, would you be able to work that out without any additional information?
The shaded part that sticks out at the top is also one of those similar triangles, right angle pointing up this time. You know that one side of that triangle is 5 and you also know that another side is 3/4 times 5. Both these sides are next to the right angle so you just multiply them with each other and divide by 2 to get the area of that triangle.
5*(3/4)*5
=5*(15/4)
=75/4
(75/4)/2=75/8
Then subtract that from 100 (the whole shaded area).
100-(75/8)
=(800/8)-(75/8)
=725/8
In middle Egypt they knew "the area of a square of 100 is equal to that of two smaller squares. The side of one is ½ + ¼ the side of the other."
I thought it interesting the shaded areas is 100 and you got b=3/4a on your working
So, knowing this here's another way of solving once you know the scale factor is 4 and have worked out the bottom left triangle:
You know the length given is 13, you also know the small triangle at the bottom left hand corner is 3,4,5. So the length of the side of the black square is 16. So because we now know the length is 16, that means the side opposite it is also 16. So 3/4 of 16 is 12 which means the other side of the triangle is length 12. 12^2 plus 16^2 is 400. Divide 400 by 4(the scale factor) and you get 100. because 3,4,5 is also equivalent to 6,8,10 and therefore 12,16,20 then you now know the hypotenuse of the triangle on the right is 20 and the hypotenuse can be divide into 4 lengths, 20/4 is 5 which gives you the hypotenuse of the bottom left triangle and then you get the areas of 25 for one square. Then you go 25*4 which is 100. which proves the Egyptians were right about a side being 3/4 the length of another
Cool!👍👍
What if I wanted the area inside the original square box?
16*16
This math guy has 3.14 lakh subscribers....... This sounds like pi..... Quite unique math lover
when i see a colorful handmade drawing, i can instantly see that is a Catriona Agg question.. bc nobody redraw the question digitally .. dont know why tho :))))
How exciting!?
Exciting.
Lat step is pythagorus
That’s what you should’ve said
The angles are very tricky.
i thought you had to cut it off at the top
Sorry wait how do you mathematically prove that both triangles angles are equivalent
They have a shared angle and a 90° angle. The third angle would have to be the same. Duh!
it would be great if you had a discord server we would love to join
How exciting
Please make a desmos music tutorial, i cant find any
why bro close this much the ceiling
Scale factor? Whats that? Anyone help
I thought this was going to be working out the area of ummmm.... on "No Love Deep Web"
Me to my neighbors kids: this looks important, let's put a box around it
I just use a ruler.
Nice
always more geometry!!!
💯
Dang, I’ve spent like 50 minutes already and I’m only 12 seconds into the video.
I feel like you skipped a step by assuming that the outer shape was a square
The problem states that there are five squares. That means the outer shape is a square.
i dont get it but looks cool
Bravo
&E,
AND E,
ANDY
...
How exciting
I did all the right steps but I didn’t do it as simple…
🎉
Follow up question.. is there enough info to solve for the red shaded area that’s within the square? 75 plus what sq units?
Would it be 96.625. By using the same method the top left triangle is also similar and we can do the area of the square minus the area of all of the triangles.
nice
Wow.
👍👍👍👍👍👍👍👍👍👍👍👍👍👍👍👍