Calculus

A rancher wants to fence in an area of 500000 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?

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  1. I will set it up for you.
    Let the length of the rectangle be y feet
    let its width be x feet. The divider will then be x feet
    So the length L
    = 3x + 2y

    but you know that xy = 500000
    and y = 500000/x

    then
    L = 3x + 2(500000/x)

    differentiate, set that equal to zero and solve for x
    Put x back into L = ...
    and you are done

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  2. 2345678

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  3. 3464.1016

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