Adairy 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?

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