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12 April, 19:19

A rectangular area is to be fenced in with 300 feet of chicken wire. find the maximum area that can be enclosed.

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  1. 12 April, 23:11
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    Let the lengths of the sides of the rectangle be x and y. Then A (Area) = xy and 2 (x+y) = 300. You can use substitution to make one equation that gives A in terms of either x or y instead of both.

    2 (x+y) = 300

    x+y = 150

    y = 150-x

    A=x (150-x) < - - (substitution)

    The resulting equation is a quadratic equation that is concave down, so it has an absolute maximum. The x value of this maximum is going to be halfway between the zeroes of the function. The zeroes of the function can be found by setting A equal to 0:

    0=x (150-x)

    x=0, 150

    So halfway between the zeroes is 75. Plug this into the quadratic equation to find the maximum area.

    A=75 (150-75)

    A=75*75

    A=5625

    So the maximum area that can be enclosed is 5625 square feet.
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