Posted by **Adam** on Saturday, May 29, 2010 at 8:34pm.

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?

- CALC -
**MathMate**, Saturday, May 29, 2010 at 10:09pm
Area to be fenced in, A = 1,500,000 sq.ft.

Width (shorter side) = x

Length (longer side) = A/x

Total length of fence, L

= 3x+2(A/x)

Differentiate with respect to x:

dL/dx = 3 - 2A/x²

To get minimum length,

dL/dx = 0

3 - 2A/x² = 0

x=sqrt(2A/3)=1000 ft.

Check that d²L/dx²>0 for L to be a minimum.

Calculate the length of fence required.

- CALC -
**Adam**, Sunday, May 30, 2010 at 1:21am
thank you so much for the clear explanation. i really understand how to do the problem now! i appreciate it!

- CALC :) -
**MathMate**, Sunday, May 30, 2010 at 8:34am
You're welcome!

- CALC -
**Kamsan**, Saturday, November 12, 2011 at 9:17pm
what is the answer of this question?

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