A rancher wants to fence in an area of 3000000 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?

Let X and Y be the two dimensions.

Area will be X times Y.

XY = 3000000

Y = 3000000 / X

Perimeter = 2x + 3y

substituting the values:

Perimeter = 2x + 3*3000000 / x

= 2x + 9000000 / x

2 = 9000000 / x^2

x^2 = 9000000 / 2 = 4500000

x = sqrt (4,500,000)

= 2121.32

= 1000 sqrt (4.5)

y = 3000000 / 2121.32

= 1414.2

= 1000 sqrt (2)

so the dimensions will be 2121.32 by 1414.2.