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11 November, 10:49

A farmer has 3000 feet of fencing to use on a new enclosure. The new enclosure will go up against existing fencing so one side does not need additional fencing. If the farmer wants to subdivide the enclosure to have 3 pens, what is the maximum total area the farmer can enclose?

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  1. 11 November, 11:17
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    375000 ft^2

    Step-by-step explanation:

    From the statement that we have that it would be 1 time the length and 2 times the width because one side is not necessary and also we must take into account that it would be divided by 3 equal enclosures therefore we will use 1000 feet (3000/3) so Therefore, the perimeter would be equal to:

    1000 = l + 2 * w

    we solve for w:

    l = 1000 - 2 * w

    Also the area is equal to:

    A = w * l

    replacing:

    A = w * (1000 - 2 * w)

    A = 1000 * w - 2 * w ^ 2

    We derive:

    A ' = 1000 - 4 * w

    Let's equal 0:

    1000 - 4 * w = 0

    w = 1000/4

    w = 250

    replacing and we calculate l:

    l = 1000 - 2 * 250

    l = 500

    A = 250 * 500

    A = 15,000 ft ^ 2

    Which means that for each subdivision the maximum area would be 125000 square feet and the total would be:

    125000 * 3 = 375000 ft ^ 2
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