```Question 381586
Suppose that you have 800ft of fencing. you are to constuct a rectangular corral which is divided into two pieces. What are the dimensions that give the largest possible area?
First, Construct a quadratic function that gives the area of the enclosure in terms of a single variable?
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Draw the picture: a rectangle with a segment parallel to a side  dividing the area.
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Let the dividing segment have length "x". (Note there are 3 segments of
length "x")
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800-3x is the remaining fence length.
(800-3x) is the length of the base and of the top of the rectangle.
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Area of the outer rectangle is x(800-3x)/2
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Simplify that Area Equation:
A(x) = (-3/2)x^2+ 400x
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That is a quadratic with a = -3/2 and b = 400
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Maximum area occurs when x = -b/2a = -400(2(-3/2)) = 400/3 = 133 1/3 ft.
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Dimensions of the corral are:
height = x = 133 1/3 ft
width: = (800-3x)/2 = (800-3(400/3))/2 = 200 ft
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Cheers,
Stan H.

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