Question

The figure shows a square region divided into four rectangular regions, three of which have areas 5x, 5x, and x^2, respectively. If the area MNOP of is 64, what is the area of square QROS?

Answer 1

5x + 5x + x^2 + ? = 64

Answer 2

I did this: \[x^2 + 2*5x + ? = 64\]

Answer 3

same thing, what's the matter?

Answer 4

haha

Answer 5

that x and ? confuse me

Answer 6

I have a different way...
do we have to solve it your way? because I want to solve it geometrically.

Answer 7

no wait!

Answer 8

I think I did it

Answer 9

\[x^2+10x+25= 64\]

Answer 10

Good job!
here's my way to see it:
if you look at the sides you can see that the length of the long sides of your figure must be 5, and the area of the short sides is x, because that is the only way to get the proper area of the smaller figures