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Answer to Question #4543 in Geometry for dolores

Question #4543
You need to enclose a 250 square foot section with a fence that costs $1.50 per yard. What dimensions would you use to minimize the cost?

Expert's answer
You need to enclose a 250 square foot section with a fence that costs $1.50 per yard. What dimensions would you use to minimize the cost?

The ratio of the magnitude of the area enclosed to the magnitude of the length of the fence would decreases as the number of sides increases, and the sides are equal in length. In other words an equilateral triangle with an area of 250 square foot would require a longer fence than a square, and so on.
The shape of the area enclosed which requires the least fencing is a circle; a circle can be taken to be a shape that is made up of infinite number of equal sides.
A circle with an area of 250 square foot has a radius of sqrt(250/pi).
To minimize costs the enclosed area should be a circle with a radius sqrt(250/pi) foot.

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