# Suppose you have 200 feet of fencing to enclose a rectangular plot. How do you determine dimensions of the plot to enclose the maximum area possible?

##### 1 Answer

The length and width should each be

#### Explanation:

The maximum area for a rectangular figure (with a fixed perimeter) is achieved when the figure is a square. This implies that each of the 4 sides are the same length and

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Suppose we didn't know or didn't remember this fact:

If we let the length be

and the width be

then

or

Let

then

This is a simple quadratic with a maximum value at the point where it's derivative is equal to

and, therefore, at it maximum value,

and, since