A square poster has sides measuring 2 feet less than the sides of a square sign. If the difference between their areas is 56 square​ feet, find the lengths of

Question

A square poster has sides measuring 2 feet less than the sides of a square sign. If the difference between their areas is 56

square feet, find the lengths of the sides of the poster and the sign

Answer 1

Let the sign have sides of length x.

Area of sign = x²

Poster has side lengths of x-2

Area of poster = (x-2)²

 

x² - (x-2)² = 56

x² - (x² - 4x + 4) = 56

4x - 4 = 56

4x = 60

x = 15 ft

 

The sign has side lengths of 15 ft

The poster has side lengths of 15-2 = 13 ft

 

Check:  15² - 13² = 225 - 169 = 56 ft²