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Math Help - Similar triangles

  1. #1
    Junior Member
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    Similar triangles

    This problem has made me feel quite embarrassed.
    AB, FE and DC are perpendiculars to BC.
    FE is 2 and AB is 6. We are looking for DC.

    I believe the solution might come using the similarity of some triangles.
    I have found that ABC and ECF are similar, hence BC=3EC.
    And BFA is similar to CFD, but I couldn't make a great use of this.
    I suppose I need to find a relation between BC and the triangle CDF... in case there is any, that is...

    If you have a different solution that does not make use of similar triangles, it is, of course, as much appreciated.
    Attached Thumbnails Attached Thumbnails Similar triangles-problem_figure.jpg  
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  2. #2
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  3. #3
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    Oh, I am sorry. I was looking at a different picture with letters placed in a different order.
    I have corrected it, I believe.
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  4. #4
    MHF Contributor Quick's Avatar
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    ABC is similar to FEC

    AB = 6, FE = 2

    So FE is 1/3 of AB.

    That means that EC is 1/3 of BC

    So then BE is 2/3 of BC

    FEC is similar to DCB

    BE is 2/3 of BC

    So FE is 2/3 of DC

    So DC = FE*3/2

    So DC = 3
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