Question

The polynomial x^2-18x+81 represents the area(in square feet) of a square courtyard. Write an expression for the perimeter of the courtyard.

Answer 1

Answer:

4x - 36 feet

Step-by-step explanation:

The area A of a  square whose sides are s units is given as

A = s * s

Given that the area A = x^2-18x+81, factorizing

A = x^2-9x-9x+81

A= x(x-9)-9(x-9)

A = (x-9)(x-9)

A = (x-9)^2

This means that the size of each side of the square  courtyard is x-9 feet long

Recall that the perimeter P of a square whose side is s long is given as

P = 4s hence since the side of the courtyard is x - 9 feet, the perimeter of the courtyard

P = 4(x-9)

= 4x - 36 feet