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
Answer:
The dimensions of the rectangle. Length= 15 inches and Width= 8 inches
Step-by-step 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
=> [tex]W^{2}+7W-120=0[/tex]
=>[tex]W^{2}+15W-8W-120=0 =>(W+15)(W-8)=0[/tex]
=> [tex]W=-15 or 8[/tex]
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
