[ASMR] I Couldn't Solve This MATH Problem... Can YOU?

4 місяці тому

Can you solve this mathematical problem that stumped me? Using algebra, geometry and more stay tuned to see the solution and relax to some ASMR Maths.
The Problem: engineers_feed/st...
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My name is Duncan and I am a Maths Graduate in Scotland with a passion for maths and relaxation! I am an ASMR UKpostsr and plan to go on to teach maths at high school level in the coming years. I am very enthusiastic about teaching and to help me improve and get practice before entering the world of work I have created this channel to help people learn about mathematics at all levels all whilst having a good night's sleep.
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КОМЕНТАРІ: 26

@voetbalkits 3 місяці тому

i always fall asleep in maths because (in my opinion) it can sometimes be very dry. so why not listen to a maths asmr video to sleep usefully

@ASMRMaths 3 місяці тому

Thanks for watching 😅

@obitorial3661 3 місяці тому

Easiest method trust: Set orange top length to X, area of 3x and therefore all areas are 3x Yellow, green and pink have area of 9x because 3(3x)=9x Since the top length of yellow, green and pink is the same as orange (x), area shows the height of yellow is 9 bc 9x/x=9 therefore one length is 3+9=12 and the squares area is 144 :D

@lowgun5181 3 місяці тому

Assign the top side of the orange rectangle a value of x The area of each rectangle is 3x The blue rectangle must be 1/5 of the width of the square, given that it extends the height of the square. Therefore, given that those other 4/5 of the width is equal to x, the missing piece is 1/4x For the blue rectangle to be the same area as the orange one, it must have an area of 3x. Given its now known width, we now know it has a height of 12. Given that the problem says the shape is a square, the area of the whole square is 144.

@spearstip9812 3 місяці тому

Let a be the length of the square's side. Orange area = 3x (let x be the unknown length) Yellow area = 1/2 (green + pink) area, but since yellow and green+pink rectangles have the same height this means Yellow width = 1/3 total width = 1/3 x so Yellow area = (a-3) * x / 3 but Yellow area = Orange area => (a-3)*x/3 = 3x => a = 12 and so the square's area is 144 :D

@marieslibrary 3 місяці тому

Thanks for making falling asleep feel smart. Great video. ✨️

@yatelevizor 3 місяці тому

It can be done differently. (Here I didn’t even use the blue rectangle at all). Since the areas of green and pink are equal and they have a common side, then the other sides are also equal because a^2 * b^2 = a^2 * c ^ 2. Therefore they are equal. Then the yellow side is divided in half. And at the same time, the area of yellow is equal to the area of green, then this can be written as d^2 + (2b) ^ 2 = a^2 + b^2, then d = 1/2a. Then the orange figure has a third side equal to 3/2a . The area of orange and yellow is equal, i.e. (1/2a)^2 + (2b)^ 2 = (3/2a)^2 + 3 ^ 2. Transforming, we get that 9/4 * 9 = 1/4 * (2b)^2. Then 2b = 9, which is the left side of the yellow rectangle, then the side of the square is 9 + 3 = 12. Answer 144

@ASMRMaths 3 місяці тому

Very interesting solution! Well done

@clara_hp6254 3 місяці тому

That's what I did too :)) Didn't take me long - The sad part was that I then didn't realise I'd solved it for another 5 minutes (i was trying to figure out the value of the yellow area to then multiply it by 5 haha

@sunxdokyeom 3 місяці тому

i love me a good asmr that makes my brain cells move lol

@Hydrochloric_ASMR 3 місяці тому

Interesting approach!

@rileygray1040 3 місяці тому

i just treated yellow, pink, and green as one big rectangle with an area 3 times that of orange. our big rectangle shares one dimension with the orange rectangle, so the factor of 3 has to come from the other dimension, i.e. the length of the yellow rectangle must be 3 times the width of the orange rectangle, which is 9. now we know the sides of the big square are 3+9, or 12, square that and you get 144.

@lowgun5181 3 місяці тому

I think this is even easier than my explanation. I only used the blue and orange rectangles and thought the math was easy but this is the easiest one yet

@u.hornung2638 3 місяці тому

The moment he said: it's a very nice number, i already knew that it was going to be 12 for x

@shirayuki2974 3 місяці тому

Separate 4 to 1, blue by itself. Top length = x. Since every area is the same, and area of top one will be denoted to 3x, bottom 3 = 9x. So length of one side is 12, 12²=144.

@larsnyeet 3 місяці тому

Super entertaining!

@eliscoelho5494 3 місяці тому

i gotta say i can’t keep clicking on your math videos before bed because i’ll ALWAYS stop everything, pause it and solve it before i can fall asleep 😂😂😂 anyways… A=144

@chrisb8698 3 місяці тому

Ha, you must have overthought this one. Almost no algebra required. Neat puzzle though.

@vevepriezviskova6909 2 місяці тому

Hi I´ve just discovered your channel, it´s great! :) Can you please make a video about prime numbers? Also, in high school, we learnt about somehing called "complex" and Imaginary numbers. I never understood what they are or what they´re good for. Could you please explain?

@travismyrick6386 3 місяці тому

Get rid of the pink, green, and yellow shapes. Replace them with 3 orange rectangles. Now you have 4 horizontal orange rectangles and one vertical blue rectangle. Multiply 3 by 4 get 12 then square that side ending up with 144.

@temporalcatcher9950 3 місяці тому

My way is not as quick nor simple, but it works. I started knowing green and pink are the same. We know this because their lengths and area are the same and therefore their height must be too. yellow’s height (y_h) is 2 times green’s height (g_h). To keep area the same, yellow’s length is half green’s length. That means orange’s length is 1.5 * green’s length (g_l) Area of orange: 3 * 1.5 * g_l = 4.5g_l Area of green : g_l * g_h since both are equal: 4.5g_l = g_l *g_h g_h = 4.5 y_h = 2g_h = 2 * 4.5 = 9 Blue’s height (and length of square) is the sun of orange’s height and yellow’s height x = o_h + y_h = 3 + 9 = 12 Area of square: x^2 = 12^2 = 144

@connorrs_ 3 місяці тому

I would draw a line to make 30-60-90 and 45-45-90 triangles and then use sine, cosine, and tangent ratios to find other lengths. guys do NOT take honors geometry

@blak5511 2 місяці тому

Honors geometry ain’t that hard

@no.own.content2712 3 місяці тому

technically it’s correct but 1/5 is the area of the blue and not the length b so the start of his invoice doesn’t make sense or am I wrong ?

@jani5243 3 місяці тому

Ur wrong, 1/5x^2 is the area of the blue rectangle and 1/5x is the length of b, as clearly shown in the video

@KyleTurpin42 3 місяці тому

We were taught never to trust the diagram to be correctly proportioned except as labeled. On that basis, I have to say there isn't enough information. The total area is 15X but we can't solve for X.