[ASMR] An Interesting Geometry Problem

Tonight, I challenge you to try and solve this interesting and fun Geometry problem involving squares and areas. With a little bit of algebra and mathematical techniques can you solve it? If not, follow along as I relaxingly explain the steps to complete the question!
Credit to andymath.com on TikTok for the inspiration to this problem
PDF: drive.google.com/file/d/1ShD9...
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✨ ABOUT ME
My name is Duncan and I am a Maths Graduate in Scotland with a passion for maths and relaxation! I am an ASMR UA-camr 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.
✏️ MATHS ENQUIRIES
For maths enquiries such as help with problems, video suggestions or areas you think would be good to cover in one of my videos please email me at [e-mail]
😴 WHAT IS ASMR?
ASMR is a tingling sensation that creates relaxation through auditory sounds, visuals and more. Click here to read more:
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#ASMR #Maths #Relaxing

[@ASMRMaths]

It's the long awaited sequel to my first Geometry Problem style video! Hope you all enjoy and let me know if you find any other methods to solving the problem 🧠

[@AngusCalvert]

I didn't understand why expanding the brackets in the second section resulted in 24y. other than that great video and well explained.

[@toastyoriginal]

You need more likes im subscribing!

[@Aghul]

@@AngusCalvert The (12 + y)² is a binomial formula and gets solved like this: (a + b)² = a² + 2ab + b²
a in this case is 12 and b is y.
The full way to solve it is:
(a + b)² = (a + b) * (a + b)
Here you solve it via the 'FOIL' method, aka 'First, Outer, Inner, Last - you multiply first the two first variables of the respective brackets, then the two outer variables, then the two inner variables, and then the last two variables of each respective bracket:
(a + b) * (a + b) = a² + a*b + a*b + b²
You can sum up the two [a*b] parts and get a² + 2ab + b²
Now in our specific case, it'd go as follows:
x² = (12 + y)² = 12² + 2*12*y + y² = 144 + 24y + y²

[@AngusCalvert]

@@Aghul thank you very much. I now understand double brackets and how to expand them

[@colin8923]

I'm working through some math problems right now, how convenient!

[@AbdullahAwadallah]

208 + 64 + 16 = 288 (total area of square without the green one)
Now we try squaring whole numbers
17²= 289 (illogical to be our full square)
18²=324 (is probably the area of our full square)
19²=361 (might be)
So we take our added up area and subtract it from our potential full square
324 - 288 = 36 (the area of our green square)
Now we know the blue is 16 in area
And Red is 64
Obviously the green is somewhere in between and 36 is definitely between them so it's 36

[@saeedwrld22]

I solved the problem since the start of the video and stay to enjoy some good asmr

[@ASMRMaths]

Awesome!

[@grace-os4eu]

Enjoyed working on this prob, it was kinda easy but really enjoyed it!

[@Pillowkasmr]

You whisper is super relaxing and your channel super original! I also do ASMR videos (but not about mathematics ahah)

[@geneash8547]

I just saw that the green box was in between them and red is 8x8 and blue is 4x4 so green is 6x6 and I added them all together

[@Waiter1986]

not how it really works. could’ve ended up with the wrong answer just by guessing it lol

[@7venxce]

there's always a possibility that the green square is not a square that has sides with integer values (for example 5.5, 5.9, etc). proving it with a solution will always be the best :))

[@Chloee_2921]

Can you please do an ASMR preparing you for geometry regions?

[@lovo3259]

Dido you should do something regarding physics

[@_stevebutwhy]

10:53 why +24y?

[@Aghul]

The (12 + y)² is a binomial formula and gets solved like this: (a + b)² = a² + 2ab + b²
a in this case is 12 and b is y.
The full way to solve it is:
(a + b)² = (a + b) * (a + b)
Here you solve it via the 'FOIL' method, aka 'First, Outer, Inner, Last - you multiply first the two first variables of the respective brackets, then the two outer variables, then the two inner variables, and then the last two variables of each respective bracket:
(a + b) * (a + b) = a² + a*b + a*b + b²
You can sum up the two [a*b] parts and get a² + 2ab + b²
Now in our specific case, it'd go as follows:
x² = (12 + y)² = 12² + 2*12*y + y² = 144 + 24y + y²

[@ireallylovelunchtime]

I just guessed the area of the green box because of the similarities in the shapes 😂

[@ASMRMaths]

That's really good initiative. It's called mathematical approximation. Here you were able to approximate the area of the green box due to other areas of maths as you mentioned! Love to hear it

[@WinterFlare]

Lol I took a look at it and was like the green box is 36 yeah? The gap between the height of the blue square to the green square is the same as the height from the green to red square. So I just assumed it was a gap of 2.

[@kaylanmisbaer7069]

Can’t wait for the stream

[@ASMRMaths]

Me too! Hope to see you there

[@mobivancauwenbergh4467]

Can you make a video about the cos. and sin. rule?

[@ASMRMaths]

Sure thing! I'll look into a trig video soon

[@Tekomain]

actualy, I've calculated the resoult, before starting the vid, but sill whatched it

[@casperk7310]

Damm i guessed the area of the green square correctly. I feel very smart now

[@ks4willbball201]

Can you please tutor me in Algebra 2

[@Tamariasmr]

😴