The width of a rectangle is (x-5) and the length is (x+2). What is the length and width of the rectangle if the area is 18 square feet?

Length: 9

Width: 2

Step-by-step explanation:

Area = length * width

18 = (x - 5) (x + 2)

18 = x² - 5x + 2x - 10

x² - 3x - 28 = 0

x² - 7x + 4x - 28 = 0

x (x - 7) + 4 (x - 7) = 0

(x - 7) (x + 4) = 0

x = 7, - 4 (not possible)

Length: 7+2 = 9

Width: 7-5 = 2

(x-5) (x+2) = 60

x^2 + 2x - 5x - 10 = 60

x^2 - 3x - 10 = 60

x^2 - 3x - 70

(x-10) (x+7)

x = 7

Proof:

x + 2

x - 5

Plug in 7.

7 + 2 = 9

7 - 5 = 2

9 x 2 = 18