Question

A square poster has sides measuring 2 feet less than the sides of a square sign. If the difference between their areas is 32 square feet. Find the lengths of the sides of the poster and the sign?

Answer 1

Area of square one = $(x-2)(x-2)$ = $x^2-4x+4$
Area of square two = $x^2$

The difference of the area of two squares = 32
$x^2-(x^2-4x+4)=32$
$x^2-x^2+4x-4=32$
$4x-4=32$
$4x=32+4$
$4x=36$
$x=36/4$
$x=9$

The side length of the poster = $x-2 = 9-2 = 7 feet$
The side length of the sign = $x=9$