Question

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

Answer 1

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.