Question

A square poster has sides measuring 2 feet less than the sides of a square sign. If the difference between their areas is 52 square​ feet, find the lengths of the sides of the poster and the sign.

Answer 1

Let $s=$ the length of a side of the sign
We get $s-2=$ the length of a side of the poster

Difference between areas is 52
So $s^{2}-(s-2)^{2}=52$
⇒$s^{2}-(s^{2}-4s+4)=52$
⇒$4s-4=52$
⇒$4s=56$
⇒$s=14$ is the length of a side of the sign

Plug into $s-2=14-2=12$ is the length of a side of the poster