A square mirror has slides measuring 2 ft less than the side

A square mirror has slides measuring 2 ft less than the sides of a square painting. If the difference between their areas is 32 ft^2. Find the length of the sides of the mirror and the painting.

Solution

Consider, X is = length of one side of the mirror

x+2 = length of one side of the painting.
area of the mirror is equal to x^2
area of the painting is equal to (x+2)^2 which is equal to x^2 + 4x + 4
difference between their areas is 32 square feet.

X^2=(X+2)^2-32
X^2=X^2+4X+4-32
X^2-X^2-4X=-28
-4X=-28
X=-28/-4

length of one side of the mirror is equal to 7.
length of one side of the painting is equal to 9.