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Math Help - Length of a side

  1. #1
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    Length of a side

    Hi,

    I am looking for nudge in the right direction with this one. Very dense at the moment.

    The Triangle XYZ is right-angled at Y and M is midpoint of XZ. Given that YZ = 5, and YM = 6.5 cm, find the length of XY.

    Length of a side-midpoint_triangle.gif

    What am I missing? I have a feeling that the M is midpoint part is crucial. But how?

    Thanks for all your help!
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  2. #2
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    Quote Originally Posted by mathguy80 View Post
    Hi,

    I am looking for nudge in the right direction with this one. Very dense at the moment.

    The Triangle XYZ is right-angled at Y and M is midpoint of XZ. Given that YZ = 5, and YM = 6.5 cm, find the length of XY.

    Click image for larger version. 

Name:	midpoint_triangle.GIF 
Views:	20 
Size:	2.2 KB 
ID:	21187

    What am I missing? I have a feeling that the M is midpoint part is crucial. But how?

    Thanks for all your help!
    Here is a hint: Prove that the midpoint of the hypotenuse of a right triangle is equidistant from the vertices.

    It then follows that XZ = 13 and so XY = 12 is easily obtained.
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  3. #3
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    Fantastic! I completely blanked out on that. I have been using "Diameter subtends a right angle on circle", but didn't think of using it in reverse. Thanks a lot, a very elegant problem and solution.
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