2. The rectangular floor of a garage has an area of 198 square feet. Andy knows that the floor is 7

feet longer than it is wide. What is length of the floor of the garage?

a. 11 feet

b. 14 feet

C. 18 feet

d. 92 feet

length = 18 ft

Step-by-step explanation:

Let w = width

L = w+7

Area = l*w

198 = (w+7) (w)

Distribute

198 = w^2 + 7w

Subtract 198 from each side

0 = w^2 + 7w - 198

Factor

What 2 numbers multiply to - 198 and add to 7

18 * - 11 = - 198

18+-11 = 7

0 = (w+18) (w-11)

Using the zero product property

w+18 = 0 w-11=0

w = - 18 w=11

We cannot have negative width so w=11

We want the length

l = w+7

l = 11+7 = 18