Math

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The area of a trapezoid is 66 sq units. The length of its longer base is 4 units longer than the length of its shorter base, and its height is 7 units longer than the length of its shorter base. Find the length of each base and the height of the trapezoid.

  • Math -

    you know that with bases b and c, and height h, a trapezoid has area

    a = h * (b+c)/2

    Just plug in your numbers, letting x be the length of the short base:

    a = (x+7) * (x + x+4)/2
    66 = (x+7)(x+2)

    x^2 + 9x - 52 = 0
    (x+13)(x-4) = 0
    x = 4

    short base = 4
    long base = 8
    height = 11

    area = 11(8+4)/2 = 11*6 = 66

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