Answer: The length of the side of the square poster is 8 feet
The length of the side of the square sign is 10 feet
Step-by-step explanation:
Let the length of one side of the square poster be x
Let the length of one side of the square sign be y
Since they are both squares, the area of a square is expressed as length^2
A square poster has sides measuring 2 feet less than the sides of a square sign. It means that
y = 2+x
If the difference between their areas is 36 square feet, it means that
y^2 - x^2 = 36 - - - - - - - 1
Substituting y = 2 + x into equation 1, it becomes
(2+x)^2 - x^2 = 36
4 + 4x + x^2 - x^2 = 36
4x = 36 - 4 = 32
x = 32/4 = 8
y = 2 + x = 2 + 8
y = 10
