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 the fence must he buy if the perimeter of the rectangle is 320 feet?

There are two possible solutions.

200 ft or 280 ft

Step-by-step explanation:

Given that the barn forms one end of the rectangle, the farmer would not need to fence that side. However, since we don't know where the end of the rectangle formed by the barn is the width or the length, than there are two possible solutions. In order to find out the possible solutions, setting up an equation to find the length and width of the rectangle is necessary:

length = 'three times the width' = 3w

width = w

Perimeter = 2 (3w) + 2w = 320

Combine like terms 6w + 2w = 320 or 8w = 320

Divide and solve: w = 40 ft

Again, the side of the barn could be the width (40ft) or the length (3x40 = 120ft). Since we don't know which one, we take the total perimeter (320ft) and subtract the width and length:

320 ft - 40 ft = 280 ft

320 ft - 120 ft = 200 ft

200 or 280 ft