The perimeter of a rectangle is 18 feet, and the area of the rectangle is 20 square feet. What is the width of the rectangle?

Perimeter is given by....

P = 2(W + L)    so we have.....

18 = 2 (W + L )  divide by 2

9 = W + L     subtract W from both sides

9 - W  = L

Now...the area "formula" is given by

A = W * L    and we have

20 = W * L      ans substituting (9 - W) for L, we have

20 = W * (9 - W)

20 = -W² + 9W   .....Rearranging this gives

W² - 9W + 20 = 0

Factoring , we have

(W - 5) (W - 4)  = 0

And settong each factor to 0, we have either W = 4 or W = 5.....(depending on how we "orient" the rectangle.....)