Math

A gardenervhas 100 meters of fencing to enclose two adjacent rectangular gardens. The gardener wants the enclosed area to be 400 sq meters. What dimensions should the gardener use to obtain this area?

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  1. If the dimensions of the whole garden are x and 2y (because there are two adjacent gardens, each x by y),

    2x+4y = 100
    2xy = 400

    or,

    x+2y = 50
    xy = 200

    since x = 50-2y,

    (50-2y)y = 200
    50y - 2y^2 = 200
    y^2-25y+100 = 0
    y = 5 or 20
    So, x = 40 or 10

    The garden is 10 by 40.

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