What is the smallest length of fencing that will be required to do this?

Question

A rancher wants to fence in a rectangular area of 16000 square feet in a field and then divide the region in half with a fence down the middle parallel to one side. What is the smallest length of fencing that will be required to do this?

Answer 1

Sides of the rectangular area: x, y

Area: xy = 16000

Fencing length, 2x, 2y, x (the middle fence): L = 2x + 2y + x = 3x + 2y

From the area equation: y = 16000/x

Plug that in L, so it becomes a function of a single variable:

L(x) = 3x + 32000/x, where x > 0

The answer will be the minimal value of L(x) over the interval x > 0. I hope this helps.