SOLUTION: Please help me solve this word problem: A square mirror has sides measuring 2 ft less than the sides of a square painting. If the difference between their areas is 32 ft square

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Question 1006415: Please help me solve this word problem:
A square mirror has sides measuring 2 ft less than the sides of a square painting. If the difference between their areas is 32 ft squared, find the lengths of the sides of the mirror and the painting.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= length of the side of the painting (in feet).
x-2= length of the side of the mirror (in feet).
x%5E2= area of the painting (in ft squared).
%28x-2%29%5E2= area of the mirror (in ft squared).
The problem says that
%28x-2%29%5E2=x%5E2-32 ,
because the difference of their areas is 32 ft squared,
and the mirror, with shorter sides, must have a smaller area.

Solving %28x-2%29%5E2=x%5E2-32 :
%28x-2%29%5E2=x%5E2-32
x%5E2-2%2Ax%2A2%2B2%5E2=x%5E2-32
x%5E2-4x%2B4=x%5E2-32
-4x%2B4=-32
-4x=-32-4
-4x=-36
x=%28-36%29%2F%28-4%29
highlight%28x=9%29
x-2=9-2 ---> highlight%28x-2=7%29
The length of the sides of the mirror is highlight%287ft%29 , and
the length of the sides of the painting is highlight%289ft%29 .