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Math Help - DEFG is a trapezoid, DH = GH, EI = FI, and HI = 15.5. Find the value of x.

  1. #1
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    DEFG is a trapezoid, DH = GH, EI = FI, and HI = 15.5. Find the value of x.

    DEFG is a trapezoid, DH = GH, EI = FI, and HI = 15.5. Find the value of x.



    A)13
    B)12
    C)15
    D)14
    E)16
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  2. #2
    Super Member Matt Westwood's Avatar
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    If you imagine taking a copy of the trapezoid, flip it round 180 degrees and place the sloping edges together, you get a rectangle. Its long edge is DE + GF and that is the same as HI + IH = 2 HI = 31.

    So now you have an equation:

    \left({\frac x 2 + 3}\right) + (2x - 12) = 31

    All you need to do is solve that equation.
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  3. #3
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    Another way of looking at it: the length of the "midline" of a trapezoid is the average of the lengths of the two bases.

    \frac{\frac{x}{2}+ 3+ 2x-12}{2}= 15.5.
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