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a rancher has 310 feet of fencing with which to enclose two rectangular corrals, both of the same size. the two corrals will share one side, and a barn forms one side of both corrals. suppose the width of each corral is X feet. express the total area of the two corrals as a function of X.

  • algebra -

    assuming the barn forms the "length" of each corral, then the total fencing used comprises three widths and two lengths.

    Letting x be the width and y the length,
    3x + 2y = 310
    y = (310-3x)/2

    the area of each corral is width * length, so the total area is 2xy

    area = 2xy = 2x * (310-3x)/2 = x(310-3x)

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