# Maximization fencing

Gold Member

## Homework Statement

A rancher has 125,000 linear feet of fencing and wants to enclose a rectangular field and then divide it into four equal pastures with three internal fences parallel to one of the rectangular sides. What are the dimensions for each of the four equal pastures that will maximize the area of each pasture?

## The Attempt at a Solution

Please see attached work. According to the back of the book, the dimension of 12,500 (green checkmark) is correct. But when I plug this value into the original equation to find the other dimension, I am getting an incorrect solution. Any ideas?

#### Attachments

• Screen Shot 2019-01-04 at 7.29.14 PM.png
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magoo

Under step, 1b, you have 4A = wl. Obviously, it should be 4A = 4wl

OK?

• opus
Gold Member
By multiplying a single side of the equation by 4, I understand that I changed the actual value of the equation. However, my reasoning is that I'm looking for 4 separate areas, each having ##(w)(l)##. So why the 4 on the RHS as well? I feel like that makes the dimensions 4 times larger than what they should be.

magoo
A represents the area of one rectangle. You have 4.

• opus
Gold Member
Yes which is why I have the 4 on the left. But wouldn't having the 4 on the right throw the dimensions of ##w## and ##l## off?

Homework Helper
The question was:

What are the dimensions for each of the four equal pastures that will maximize the area of each pasture?
But you gave the length of the big rectangle.

• opus
Gold Member
Ohh I see. Thank you guys. Then the second part should be 7812.5 ft.