Chapter 4.4, Problem 10E

To determine

To find: The dimension for which the outer rectangle will require the smallest total length of fence.

Answer to Problem 10E

The dimension of the outer rectangle are

And of fence will be needed.

Explanation of Solution

Given information: Area of the rectangular pea patch is

Formula used:

Area of the rectangle,

Calculation:

Area of the rectangle,

  

The area is,

  

The amount of fence needed is,

  

Taking first and second derivative we get,

  

  

Assume,

That is,

  

Implies,

  

Now,

  

Thus, at there is a minimum.

Now,

  

The dimension of the outer rectangle are

Thus, of fence will be needed.