Word Problem

Question

The length of a rectangle is
3 m
less than twice the width, and the area of the rectangle is
27 m2
. Find the dimensions of the rectangle.

Answer 1

Colin,

Let w = width of the rectangle

      l = length of the rectangle = 2w-3

Area = wl = w(2w-3) =2w² - 3w = 27 m²

 

So solve 2w2 -3w -27 = 0 for w using the quadratic formula

w = (-(-3)  +-  ((-3)² - 4(2)(-27))^.5 )/ 2 (2)

w = (3  +- (225)^.5) / 4 , but the square root of 225 is 15

w = (3  +- 15)/4 = 18/4 & -12/4 = 4.5 m & -3 m, but the NEGATIVE solution is impossible for a width, so

w = 4.5 m  and length l = 2(4.5)-3 = 6 m.

And the area = wl = 4.5 (6) = 27 m² which checks out the solution.

 

 

Answer 2

l = 2w - 3

 

A = lw = (2w-3)w = 2w² - 3w = 27

 

2w² - 3w - 27 = 0

 

At this point we can choose to use the quadratic formula or attempt factoring.  I will attempt factoring:

 

2w² + 6w - 9w -27 = 0

 

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

 

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

 

w = -3 or w = 9/2

 

Since w has to be positive, w = 9/2 = 4.5 m

 

So, l = 2(4.5) - 3 = 6 m

 

It is a 6 m x 4.5 m rectangle.