What are the lengths of the sides of the mirror and the painting?

Question

A square mirror has sides measuring 2 feet less than the sides of a square painting. If the difference between their areas is 32 square feet, find the lengths of the sides of the mirror and painting. 

Answer 1

painting has side S

mirror has side S-2

S^2-(S-2)^2=32

S^2-S^2+4S-4=32

4S-4=32

4S=36

S=9 feet for the painting

9-2=7 feet for the mirror

81-49=32