Question

A farmer wishes to fence a rectangular area behind his barn. The barn forms one end of the rectangle and the length of the rectangle is three times the width. How many linear feet of fence must he buy if the perimeter of the rectangle is 320 feet?

Answer 1

1. The formula for calculate the perimeter of a rectangle, is:

P=2L+2W

P is the perimeter of the rectangle (P=320 feet).
L is the lenght of the rectangle.
W is the width of the rectangle.

2. The problem says that the length of the rectangle is three times the width, so you have:

L=3W

3. When you substitute L=3W and P=320, into P=2L+2W, you obtain:

P=2L+2W
320=2(3W)+2W
320=6W+2W
8W=320
W=320/8
W=40 feet

4. The barn forms one end of the rectangle. Therefore the linear feet of fence (x) is:

x=P-W
x=320 feet-40 feet
x=280 feet

How many linear feet of fence must he buy?

The answer is: 280 feet