We have that the area of the outer square is equal to 14^2 plus the area of 4 right triangles with hypotenuse ab. On the other hand, from the image, it can be seen that the area of the outer square is equal to the area of 4 right triangles with hypotenuse ab plus the gray area. Therefore, the gray area measures 14^2 = 196.
Svetlash1234
@jl23k45jv
check_circle Correct
2 months ago
196
its a bitch to layout the reasoning, but confident its correcto
VI
@vii
2 months ago
I got 14, I know it exists in a square, but it should be specified for the sake of completeness.
I made a mistake by writing (ab)^2 instead of (a+b)^2, silly mistake.
Schmu
OP
@schmuman
2 months ago
You're saying the grey area is 14?
VI
@vii
2 months ago
14^2, silly mistake
eyetest
@eyetest
2 months ago
yep
Justin
@bebemaster
check_circle Correct
1 month ago
Problem needs to state that the outside figure is a square otherwise it's not possible.
"Easy" solution is to use the fact that there IS an answer (otherwise it wouldn't be a question) and rotate 90 degrees by setting the rectangles to be x by 0, and 0 by x. Their area is now 0 and the remaining grey area is 14 by 14 so 196. Proving that this is the area for all rotations is harder.
Schmu
OP
@schmuman
1 month ago
Thanks for pointing it out. I was wondering why I mentioned the figure being a square in the original wording a long time ago and now I remember haha
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its a bitch to layout the reasoning, but confident its correcto
I made a mistake by writing (ab)^2 instead of (a+b)^2, silly mistake.
"Easy" solution is to use the fact that there IS an answer (otherwise it wouldn't be a question) and rotate 90 degrees by setting the rectangles to be x by 0, and 0 by x. Their area is now 0 and the remaining grey area is 14 by 14 so 196. Proving that this is the area for all rotations is harder.