Question

The polynomial x^2 - 30x + 225 represents the area (in square feet) of a square courtyard.

Part 1: Factor the expression and write a polynomial that represents the side length of the courtyard.
Part II: Use the answer from Part I to write an expression for the perimeter of the courtyard.

Answer 1

Explanation:

`x^2-30x+225\\ \\ (x-15)^2, $ so the length of a side is 15ft. $ \\ \\ P=4x=4(15)=60, $so the perimeter is 60ft. $`

Answer 2

Given polynomial:

• x² - 30x + 225

Part I

• x² - 30x + 225 =
• x² - 2*15*x + 15² =
• (x - 15)²

Side length is

• (x - 15) ft

Part II

Perimeter of the square:

• P = 4(x - 15) = (4x - 60) ft