Question

The width of a rectangle is 7 inches less than its length. The area of the rectangle is 120 square inches. Solve for the dimensions of the rectangle. Length: inches Width: inches

Answer 1

The dimensions of the rectangle. Length= 15 inches and Width= 8 inches

Explanation:

Let width of rectangle be W and length be L then

L=W+7 ---- (A)

Also given that area of rectangle = 120 square inches

=> WxL=120 -----(B)

From equation (A) and (B)

Wx(W+7) = 120

=>
`W^(2)+7W-120=0`

=>
`W^(2)+15W-8W-120=0 =>(W+15)(W-8)=0`

=>
`W=-15 or 8`

Since the width can not be a negative quantity , so W= 8 inches

=> L= W+7= (8+7) inches = 15 inches

Thus the dimensions of the rectangle. Length= 15 inches and Width= 8 inches

Answer 2

area = L x W

W=L-7

120 = L x L-7

120 = L^2-7L

L^2-7L+120 =0

(L-15) (L+8)

L=15, L=-8. It can't be a negative number so L=15

W=15-7 = 8

15*8 =120

length = 15 inches

width = 8 inches