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20 May, 14:13

The owner of the Rancho Grande has 3,060 yd of fencing with which to enclose a rectangular piece of grazing land situated along the straight portion of a river. If fencing is not required along the river, what are the dimensions (in yd) of the largest area he can enclose?

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  1. 20 May, 14:36
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    1170450 yd^2

    Step-by-step explanation:

    The first thing is to calculate the necessary perimeter, which would be like this:

    2 * a + b = 3060

    if we solve for b, we are left with:

    b = 3060-2 * a

    Now for the area it would be:

    A = a * b = a * (3060-2 * a)

    A = 3060 * a - 2 * a ^ 2

    To maximize the area, we calculate the derivative with respect to "a":

    dA / da = d [3060 * a - 2 * a ^ 2

    ]/gives

    dA / day = 3060 - 4 * a

    If we equal 0:

    0 = 3060 - 4 * a

    4 * a = 3060

    a = 3060/4

    a = 765 and d

    Therefore b:

    b = 3060 - 2 * a = 3060 - 1530 = 1530

    A = a * b

    A = 765 * 1530

    A = 1170450 and d ^ 2
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