Geometry: The length of a rectangle...?

Question

The length of a rectangle is 3cm longer than twice its width. The area of the rectangle is 90cm^2. Find the length and width of the rectangle.

Answer 1

let x be the width
2x + 3 is the length

area = width * length
90 = x(2x+3)
90 = 2x^2 + 3x
2x^2 + 3x - 90 = 0

factor
(x-6) (2x + 15)

x= 6 or -15

since distance can not be negative, 6 is your answer

width = 6cm
length = 6*2+3 = 15cm

Answer 2

L = 2W + 3
A = L*W
90 = (2W+3)W
90 = 2W^2 + 3W
0 = 2W^2 + 3W - 90
0 = (2W+15 )(W-6)
W = 6 (width can't be a negative)
L = 2W+3 = 2(6)+3 = 15