Question

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

Answer 1

Answer:

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=2b2+8b=120 =>

2b2+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

Answer 2

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 ))