Question

The polynomial x^2 - 22x + 121 represents the area (in square feet) of a square courtyard. a.) write a polynomial that represents the side length of the courtyard.

b.) Write an expression for the perimeter of the courtyard.

Answer 1

Explanation:

Since the court yard is square in nature, the area of the court yard will be exprerssed as;

A = Length * Length

A(x) = L²

Given area of the court yard A(x) = x^2 - 22x + 121

x^2 - 22x + 121= L²

Factorizing the quadratic expression

(x^2 - 11x) -(11x+ 121) = L²

x(x-11)-11(x-11) = L²

(x-11)(x-11) = L²

(x-11)² = L²

Square root both sides to the length of the courtyard

√(x-11)² = √L²

L = x-11

Hence the length of the courtyard is (x-11)ft

b) The perimeter of the courtyard P = 4L

P = 4(x-11)

P = 4x - 44

Hence an expression for the perimeter of the courtyard is 4x-44 feet