Solving a word problem using a quadratic equation with rational roots

Question

The area of a rectangle is 54ft^2, and the length of the rectangle is 3ft more than twice the width. Find the dimensions of the rectangle. 

 

Length: ____ ft

Width: ____ ft 

Answer 1

Since we know Area = length x width for this one we have

L = 2w + 3

Area = w(2w + 3) = 2w² + 3w

54 = 2w² + 3w

This can be expressed as the quadratic equation below

0 = 2w² + 3w - 54

Using factors of 54 and 2 which include 1,2, 3, 6, 9, 18, 27, 54

We use the combination that gives a sum of or difference of positive 3

(2w - 9)(w + 6 )=0

w cannot be -6

w = 9/2 or 4.5 ft

Using the original substitution for the length,

L = 2(4.5) + 3

L = 9 + 3

L = 12 ft

Length 12 ft

Width 4.5 ft

12(4.5) = Area = 54

I hope this helps please send me a message if you have any questions.