A rectangle with an area of 120 in2 has a length 8 inches longer than two times its width. What is the width of the rectangle

6 inches

Explanation:

Area of a rectangle with length, l and breadth, b = l⋅b

Given l=2b+8 and A=120

Area A = l⋅b = (2b+8) ⋅b=2 b2 + 8b=120 = >

2 b2 + 8b-120=0 = > b2 + 4b-60=0 = > b2 + 10b-6b-60=0 = > b (b+10) - 6 (b+10) = 0 = > (b-6) (b+10) = 0; = > b=6 as b cannot be - 10.

Width is 6 inches

L x W = 120

L = 2 x W + 8

(2W + 8) x (W) = 120

2W^2 + 8W = 120

W^2 + 4W - 60 = 0

(W + 10) x (W-6) = 0

W = - 10, 6

((shouldn't be negative, so therefore W = 6))