Question

The area of a rectangular wall of a barn is 234 square feet. Its length is

8 feet longer than twice its width. Find the length and width of the wall of the

Answer 1

• length: 26 ft
• width: 9 ft

Explanation:

Let w represent the width of the wall. Then the length is 2w+8, and the area is the product of these dimensions:

234 = w(2w+8)

Dividing by 2, we can simplify this to

117 = w² +4w

We can add 4 to each side to complete the square, then take the square root.

121 = w² +4w +4 = (w+2)²

11 = w+2 . . . . . . . we are only interested in the positive square root

9 = w . . . . . subtract 2

2w+8 = 2·9 +8 = 26 . . . . . this is the length

The length and width of the wall are 26 ft and 9 ft, respectively.