The area of a rectangular patio is 126 square feet. If the length of the patio is 4 feet more than two its width, find the length and width of the patio

Question

The area of a rectangular patio is 126 square feet. If the length of the patio is 4 feet more than two its width, find the length and width of the patio

Answer 1

Hi Chez,

 

I assume you meant to say that the length of the patio is 4 feet more than two TIMES its width. If that is the case, then, let w be the width. Then, the length is 2w + 4. The area = length X width.

 

A = length X width

 

A = (2w + 4)(w) = 2w² + 4w

 

But, A = 126. We need to solve a quadratic for w.

 

2w² + 4w = 126

 

Divide through by 2 for more simplicity.

 

w² + 2w = 63 

 

w² + 2w - 63 = 0

 

(w + 9)(w - 7) = 0

 

w = -9, w = 7

 

But, we are talking about lengths, so we must have positive answers, so we can discard w = -9 as unphysical.

 

So, w = 7 feet.

 

Length = 2w + 4 = (2)(7) + 4 = 14 + 4 = 18 feet

 

Width = 7 feet, Length = 18 feet