Is the existing section however long you need it to be?

Any rectangle must have a length L and a width W. For the perimeter to be , must be equal to .

We know that by the definition of a rectangle, the section of pre-existing fence will be equal in length to either the length or the width. So, we set equal to .

This gives us , or .

Also, we know that the maximum area of any rectangle is actually a rectangle with four equal sides. This is also known as a square.

With that knowledge, when looking for the maximum area we can say that .

If , and , then .

After that, it's just basic algebra.

We know the width, and since all the sides are equal, we can square it to find the area.