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A veterinary clinic plans to build four identical dog kennels along the side of its building using 210 feet of fencing. (See the picture.) What should be the dimensions of each kennel to maximize the enclosed area? (Note: No fencing is needed along the side of the building.)

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sqdancefan
The area is maximized when half the fence is used parallel to the building, and the other half is split between the ends and partitions.

Each of the 4 kennels is (105/4)' long by (105/5)' wide, that is ...
.. 26.25 ft long by 21 ft wide.

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Let x represent the length of fence used parallel to the building. Then the total area is
.. A = x*(210 -x)/5
This is the equation of a parabola with its vertex at x=105, halfway between the zeros at x=0 and x=210.

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