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March 25, 2017

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I've tried this many times, but I keep getting a really big answer.

A rancher wants to fence in an area of 2500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?

  • math - ,

    A = a b so b = A/a

    P = 2 a + 3 b

    P = 2 a + 3 A/a

    now A=2.5*10^6
    P = 2a + 7.5*10^6/a
    dP/da = 0 at in or max
    dP/da = 0 = 2 -7.5*10^6/a^2
    a^2 = 3.75*10^6
    a = 1.936*10^3
    then b = 2.5*10^6/1.936*10^3
    b = 1.291*10^3
    P = 2*a+3*b = 7.745*10^3

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