Algebra 2

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A farmer wants to enclose three sides of a rectangular area that borders a creek. He has 2400 meters of fencing material. What is the maximum area that can be enclosed by the fence?

  • Algebra 2 -

    Let L be the length of fence parallel to the river.

    A = L*(2400-L)/2 = 1200L - L^2/2
    dA/dL = 0 = 1200 - L (using calculus)
    L = 1200 m for maximum A
    Amax = 1200*600 = 720,000 m^2

    You can get the same answer by completing the square.

    A = -(1/2)(L^2 -2400L + 1,440,000) + 720,000
    = (-1/2)(L-1200)^2 + 720,000

    That obviously has a maximum value when L = 1200.

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