Posted by **Salman** on Friday, November 6, 2009 at 8:19am.

A rancher wants to fence in an area of 500000 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?

- Calculus -
**Reiny**, Friday, November 6, 2009 at 8:41am
I will set it up for you.

Let the length of the rectangle be y feet

let its width be x feet. The divider will then be x feet

So the length L

= 3x + 2y

but you know that xy = 500000

and y = 500000/x

then

L = 3x + 2(500000/x)

differentiate, set that equal to zero and solve for x

Put x back into L = ...

and you are done

- Calculus -
**lkl**, Thursday, November 29, 2012 at 12:01pm
2345678

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