Question

A dairy farmer plans to enclose a rectangular pasture adjacent to a river. to provide enough grass for the herd, the pasture must contain 128 square meters. no fencing is required along the river. what dimensions will use the least amount of fencing?

Answer 1

To solve this problem you must follow the proccedure shown below:

 1. You have that the pasture must contain 128 square meters and no fencing is required along the river. Then:

 A=LxW

 A is the area 
 L is the lenght
 W is the width

 2. Let's clear W:

 W=A/L
 W=128/L

 3. The formula of the perimeter is:

 P=2L+W

 P=2L+(128/L)

 4. Now, you must derivate:

 dP/dL=0

 2+(128/L²)=0
 L=8 meters

 W=A/L
 W=128/8
 W=16 meters