A farmer wishes to enclose the maximum possible area with 100 meters of fence.
geometry/fence
Problem
A farmer wishes to enclose the maximum possible area with 100 meters of fence. The pasture is bordered by a straight cliff, which may be used as part of the fence. What is the maximum area that can be enclosed?
Show solution
A circle is the plane figure with highest ratio of area to perimeter. The cliff can be used to bisect a circle of radius 100/pi meters. By symmetry, this will form the pen of largest area. The resulting pen will contain 5000/pi meters squared.