A gardener has 1000 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing. What is the shortest and longest side and area?

Question

greatest area

Answer 1

Let L = length of the fencing parallel to the river

Let W = the other two sides' widths

2W + L = 1000

L=1000-2W

If you want the maximum area that can be fenced, then

A=LW = (1000-2W)W = 1000W -2W^2

A'=1000-4W = 0

4W = 1000

W = 250 feet

L=1000-2(250) = 500 feet

A=LW = 250 x 500 = 125,000 square feet