barn square feet 9 21

Question

The area of a rectangular wall of a barn is
168
square feet. Its length is
10
feet longer than twice its width. Find the length and width of the wall of the barn.



width=____ feet

Answer 1

Jessica,

 

Let L be the length of the wall and W be the width. The area is 168 sq ft, so

 

LW = 168.

 

You also know that L = 10 + 2W. Plug this in for L in the first equation and solve for W:

 

(10 + 2W)W = 168

 

10W + 2W² = 168

 

2W² + 10W − 168 = 0

 

W² + 5W − 84 = 0.

 

This can be factored as 

 

(W + 12)(W − 7) = 0,

 

so

 

W + 12 = 0 or W − 7 = 0, ans solving both equations for W, you get the solutions

 

W = −12 or W = 7.

 

The first solution clearly makes no sense (width cannot be a negative number), so the width is 7 ft. The length can be found by plugging W = 7 into either of the original equations and solving for L. Using LW = 168, you have 

 

W = 168/7 = 24 ft.

 

The answers are the length is 24 ft and the width is 7 ft.