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