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A rancher wants to fence in an area of 1500000 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?

  • CALC - ,

    Area to be fenced in, A = 1,500,000 sq.ft.
    Width (shorter side) = x
    Length (longer side) = A/x

    Total length of fence, L
    = 3x+2(A/x)

    Differentiate with respect to x:
    dL/dx = 3 - 2A/x²

    To get minimum length,
    dL/dx = 0
    3 - 2A/x² = 0
    x=sqrt(2A/3)=1000 ft.

    Check that d²L/dx²>0 for L to be a minimum.

    Calculate the length of fence required.

  • CALC - ,

    thank you so much for the clear explanation. i really understand how to do the problem now! i appreciate it!

  • CALC :) - ,

    You're welcome!

  • CALC - ,

    what is the answer of this question?

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