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`