Beautiful SAT ACT Math Question

#shorts #maths

This is a real cool practice question I ran into.

[kevinstreeter]

There is an easier way. Look the triangle in the upper left. One side is b. The other side is b-(b-a) = b-b+a = a. a^2 + b^2 = c^2 which is the area of the big square.

[Hexagon]

It’s A
I figured the shorter leg is A and i used Pythagorean Theorem to find what C^2 (the area in terms of c) is. It’s way easier and faster yk.

[GalGreen]

There's an easier way:
The area = c^2
and
c = sqrt(a^2 + b^2)

so
The area = sqrt(a^2 + b^2)^2

and the square cancels the square root, so it's just
The area = a^2 + b^2

[kimliensilva]

Wow that was really fun to watch getting broke down and solved

[bradley]

I did it in my head but I made a mistake not squring the a²

[zxp_perpendicular]

It's too easy
Let any triangle (i.e triangle with height a and base b
So, it's a right angle triangle
Therefore, c^2= a^2 + b^2 (using Pythagoras theorem)
And we know that c^2 is area so
therefore we can also say that a^2 + b ^2 will be the area of this triangle ( in terms of a and b)

[TheEulerID]

That's an overly complicated way of answering this question.

Observe that in the right angle triangle c^2=a^2+b^2 (using Pythagoras's theorem). But the square has area c^2. Therefore the area is a^2+b^2.

[johnbauman]

Now do the President Garfield proof and the Chou Pei proof.

[LetitbeLiterary]

wouldnt it be b-a-(b)? That would give -a as one of the side length of the triangle

[gregoryallen]

How do you know that all four triangles have the same area? Sure they look congruent but can you can't assume they are unless you can prove it.

For that matter, how do you know that all the interior angles are right angles? If they are then the answer is easy since that would force all four interior segments to be diagonals which means a - b has to be 0.

[buchucraft]

i love math. i just do. if math ws a woman, she would be my crush lol.

[Anonymous-]

Bro literally the question can be solve in 5 seconds. It’s already mentioned that there is an inner square and big square. And it’s already given as c. Just multiply c with c. ALL DONE. NO NEED TO MAKE IT HARDER THAN IT HAS TO BE. SMH

[imonkalyanbarua]

Why would it not be c^2? If one of the edges of the square is "c", it should be c^2.