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March 25, 2017

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Charles wants to build a vegetable garden such that three sides of the garden are fenced and the fourth side of the garden will be the existing back fence. He has 30 feet of fencing available. Find the dimensions of the garden that will produce the maximum enclosed area

  • algebra 1 - ,

    area = A = L * B where L is length and B is width

    Say back wall is one length
    then
    30 = L + 2B
    or
    L = 30 - 2 B
    then
    A = (30-2B)* B
    A = -2B^2 + 30 B
    That is a downward opening parabola (sheds water)
    We want the axis of symmetry which contains the vertex which is at the top (maximum A)
    So complete the square
    B^2 -15 B = - A/2
    B^2 - 15 B + 225/4 = -A/2 + 225/4
    (B-15/2)(B-15/2) = -A/2 + 225/2
    B = 15/2 = 7.5 feet
    L = 30 - 2(7.5) = 15 feet

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