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