Question

A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side.
What is the shortest length of fence that the rancher can use?

Answer 1

let each of the 2 equal sides by x
let yeach of the 3 equal sides by y
xy = 1,500,000
y = 1500000/x

let the length be L
L = 2x + 3y
= 2x + 4500000/x
dL/dx = 2 - 4500000/x^2
= 0 for a min of L
2x^2 = 4500000
x^2 = 2250000
x = 1500

then y = 1500000/1500 =1000

so L = 2(1500) + 3(1000) = 6000 ft

Answer 2

.000000000000001 feet or perhaps the length of the width of a cow. :)

The problem does not make much sense as stated. You could make the field extremely longs and not at all wide and divide it with a little fence in the middle the length of your very short ends.

Answer 3

Oh, sorry, I thought you meant just the length of that splitting fence.