You have 72 feet of fencing to enclose a rectangular plot that borders on a river. if you do not fence the side along the river, find the length and width of the plot that will maximize the area

The area is maximized when half the fence is used along the river. The length and width of the plot are 36 ft and 18 ft.

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Let x represent the length of fence parallel to the river. Then the area (A) can be described by
.. A = x(72 -x)/2
This equation describes a downward-opening parabola with zeros at x=0 and x=72. Its vertex (maximum) is halfway between the zeros, at x=36.