The back of toms property is a creek. Tom would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a corral. If there is 860 feet of fencing available, what is the maximum possible area of the corral?

Question

Mathematics

Bradyn

18 September, 12:35

The back of toms property is a creek. Tom would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a corral. If there is 860 feet of fencing available, what is the maximum possible area of the corral?

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Niko Owen · Answer 1

Answer: The maximum area that could be enclosed would be 92,450 square feet.

To find the maximum area, we have to write an equation relating the different sides. For our shape, we will have 2 widths and 1 length that runs parallel to the creek.

Let the widths equal x. Then, the length would be 86 - 2x.

So the area of the shape is: A = x (860 - 2x)

This is a quadratic equation with a vertex at (215, 92450).

Therefore the width should be 215 to get the maximum area of 92,450 square feet.