Solving a word problem using a quadratic equation with rational roots

Question

The length of a rectangle is
3 ft
less than double the width, and the area of the rectangle is
27 ft^2
Find the dimensions of the rectangle.

Answer= 

Length: ___ ft

Width:  ____ ft 

 

Answer 1

Let w = the width

Let 2w-3 = the length

A = lw

A = w(2w-3)

27 = 2w² - 3w

2w² -3w - 27 = 0

(2w - 9)(w + 3) = 0

2w - 9 = 0     or    w + 3 = 0

2w = 9          0r w = -3, not a logical answer

w = 4 1/2 feet

2w - 3 = 2(9/2) - 3

length = 6 feet