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Math Help - Dimensions of a triangle formed from another right angled triangle

  1. #1
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    Dimensions of a triangle formed from another right angled triangle

    Hi Everyone,
    A right angled triangle has a base of AC, the vertical is AB and the hypotenuse is BC.
    Draw a line parallel to the base, from BC/2 intersecting vertical AB.
    How can I find the lengths of the base and vertical of this smaller right angled triangle?
    Thanks.
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  2. #2
    Member HappyJoe's Avatar
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    First thing to do is to notice that the two triangles are similar. To do this, you could argue that their angles are pairwise equal.

    Then you need to apply what you know about similar triangles, namely that the ratio between a pair of corresponding sides is always the same, no matter which pair you consider. In particular, you know that the ratio between the hypotenuse of the big triangle and the hypotenuse of the small triangle is 2.

    Hope this helps. Otherwise, feel free to ask again.
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  3. #3
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    Somehow missed considering the ratios.
    Calculating a few triangles now.
    Thanks for your help.
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  4. #4
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    Hi Timmy,
    Make a sketch and mark the parallel DM. Which triangles are similar and what is the ratio of sides. Example compare sides DM and AC
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