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Thread: Triangle Question Regarding Altitude and Segment Lengths

  1. #1
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    Triangle Question Regarding Altitude and Segment Lengths

    RE is an altitude of triangle RST. Find the measures of MN, NE, and RT.

    Triangle Question Regarding Altitude and Segment Lengths-capture.jpg

    I would appreciate it deeply if someone could help me figure out NE and RT. I already know that MN is 14, but I don't know how to find the two other segments.
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    Re: Triangle Question Regarding Altitude and Segment Lengths

    One thing you haven't said is that, in order for the length of NM to be 14, NM must bisect RS, RT, and RE. Further, each side of the triangles NME and NMR is half the length of a corresponding side of RST.
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    Re: Triangle Question Regarding Altitude and Segment Lengths

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    Quote Originally Posted by HallsofIvy View Post
    One thing you haven't said is that, in order for the length of NM to be 14, NM must bisect RS, RT, and RE. Further, each side of the triangles NME and NMR is half the length of a corresponding side of RST.
    It is hard to see, but bisections are given in the attached figure.
    Quote Originally Posted by candaceformosa View Post
    RE is an altitude of triangle RST. Find the measures of MN, NE, and RT.

    Click image for larger version. 

Name:	Capture.JPG 
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    I would appreciate it deeply if someone could help me figure out NE and RT. I already know that MN is 14, but I don't know how to find the two other segments.
    Moreover, there are several similar triangles. Find them and find the lengths.
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    Re: Triangle Question Regarding Altitude and Segment Lengths

    NE is the hypotenuse in a right triangle

    one leg is 9 (half of 18)

    the other leg = 12 (half of 24)

    so NE=15
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