Question

The area of a rectangular wall of a barn is 108 ft.² its length is 6 feet longer than twice its width find the length and width of the wall of the barn

Answer 1

• 18 ft long
• 6 ft wide

Explanation:

You want the dimensions of a barn wall that is 6 ft longer than twice its width, and has an area of 108 ft².

Setup

If the width is w, then the length is (2w+6). The area is the product of these dimensions:

A = LW

108 = (2w +6)(w)

Solution

Dividing by 2, we have ...

w² +3w = 54

We can complete the square by adding (3/2)² = 2.25 to both sides:

w² +3w +2.25 = 56.25

(w +1.5)² = 56.25

Taking the positive square root gives ...

w + 1.5 = 7.5

w = 6 . . . . . . . . . subtract 1.5

(2w +6) = 2·6 +6 = 18

The length of the wall is 18 ft; the width is 6 ft.