# Thread: Find the shortest length of fence....

1. ## Find the shortest length of fence....

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?

I can see that 3x + 2y = The length we want

and that xy = Area....

but where do I go from here?

2. Originally Posted by derekjonathon
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?

I can see that 3x + 2y = The length we want

and that xy = Area....

but where do I go from here?
xy = 1500000

solve for x in terms of y or y in terms of x (your choice), and substitute into your length equation to get L in terms of a single variable. Take the derivative and minimize.

I recommend you visit this site ...

http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/maxmindirectory/MaxMin.html

... to gain some knowledge of optimization using calculus.