A farmer wants to enclose a rectangular lot that is five times as long as it is wide. One of the shorter sides of the lot is adjacent to a barn and does not require fencing. The farmer plans to fence the other three side. If the farmer has 264 ft of fencing available, what should the dimensions of the lot be?

Question

anonymous · Answer

let:
w = width of the rectangular lot
5w = length of the rectangular lot

Perimeter, P = 264 ft.

we will use the formula of a the perimeter of the rectangle to solve for the dimensions of the lot

P = 2L + 2w
substituting,
264 = 2(5w) + 2w
264 = 10w + 2w
264 = 12w
w = 264/12
w = 22 ft.

to get the length, we just have to plug in the value of w to 5w - length of the rectangular lot
5w --> 5(22) --> 110 ft.

now let's check:
P = 2L + 2w
P = 2(5*110) + 2(22)
P = 264 ft.

this makes sense! :)

the dimensions of the lot are 22 ft. and 110 ft.