Math CentralQuandaries & Queries


Question from Koleen, a parent:

How much fencing do I need for an 56,850 parcel of land for a 15 stable horse barn


The answer depends on the shape of the parcel, not just its area. Is it a rectangle? If so what are the side lengths?


Koleen wrote back

It is for a school project on how to spend a million dollars make it rectangle please


By a "56,850 parcel of land" I expect you mean a parcel of land with an area of 56,850 square feet. There are many rectangles with area 56,850 square feet and different perimeters. For example a rectangle with length 56,850 feet and width 1 foot has an area of $56,850 \times 1 = 56,850$ square feet. Its perimeter is the sum of the lengths of its sides so the perimeter is $56,850 + 1 + 56,850 + 1 = 113,702$ feet. Not a very practical parcel of land for a stable of horses.

Better dimensions might be 50 feet by 1,137 feet or 150 feet by 379 feet. If fact in fact any two positive numbers $L$ and $W$ such that $L \times W = 56,850$ can serve as the length and width of the rectangle in feet. It's your choice.


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