Help PLEASE and Explain it. Thank You!

Question

Erica wants to put bushes up along the sides of his rectangular garden. If the width of the garden is 3 feet less than the length and the area of the garden is 108 square feet, what is the width of Erica's garden?

A.12 feet

B.108 feet

C.9 feet

D.27 feet



Answer 1

Area =108

It is a rectangle so Length time Width equals Area L x W = A

The width is three feet less than the length. (W+3) = L

Substitute (W+3) for L and use the area formula

(W+3) (W)= 108

W^2 +3W=108

W^2 +3W-108=0

To factor this we two numbers that multiply to equal -108 and subtract to equal 3

(-9 x 12) = 108 and -9+12= 3

(W+12)(W-9)=0

Set both factors to equal to 0 and solve.

W+12=0 W=-12 This won't work because the answer can not be negative.

W-9=0 W=9 This one works. The width is 9 the length is 12