# You have 500-foot roll of fencing and a large field. You want to construct a rectangular playground area. What are the dimensions of the largest such yard? What is the largest area?

##### 1 Answer

A square of

Area =

#### Explanation:

Upon investigation you will discover that the greatest area for any particular circumference is that of a square.

So the length of one side is

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Lets the lengths of the sides be

Thus

Area

As the

However, we need to write

using part of the proces of completing the square we have:

Substitute this back into