# Geometry

A horse breeder wants to construct a corral next to a horse barn that is L=16 feet long, using the barn as part of one side of the corral as shown in the figure above. The breeder has 280 feet of fencing available.

Find the value of x which maximizes the amount of area the corral can enclose

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3. 👁 348
1. no figure?

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2. Since 16 feet of fencing is not used, it is the same as if a complete rectangle of perimeter 296 were being built.

The maximum area will be for a square of side 296/4 = 74 feet.

To work it out, let x be the side with the barn in it. Then we have

2x-16+2y=280
x+y=148

the area is

a = xy = x(148-x) = 148x-x^2
the vertex is at x = -b/2a = 74

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