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?
The length and width should each be
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
Suppose we didn't know or didn't remember this fact:
If we let the length be
and the width be
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,