A rancher wants to fence in a rectangular area of 18200 squa

A rancher wants to fence in a rectangular area of 18200 square feet in a field and then divide the region in half with a fence down the middle parallel to one side. What is the smallest length of fencing that will be required to do this?

ANSWER:_________feet.

Solution

Let the length of rectangle be x

Let the width be y

So, Given x*y = 18200

Total length of fence = 2x+2y +x = 3x +2y

substitute y from : y = 18200/x

So, fence L = 3x + 2(18200)/x

For smallest length : find L\' =0

L(x) = 3 - 36400/x^2 =0

x^2= 36400/3

x = 110.15 ft

y =18200/x = 165.23 ft

So, Total lenght of wire = 3x +2y = 660.90 ft