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March 24, 2017

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Find KN and LM. In triangle LKM, angle L is bisected. Line segment LK is 11, line segment KN is x-4, line segment NM is 5.4, and line segment LM is 2x + 1.3
(there is a drawing of this triangle)


Thanks.

  • Geometry-8th gr - ,

    I assume the bisector of angle L is LN where N is on KM

    In the Post
    http://www.jiskha.com/display.cgi?id=1359738761
    I proved for you , and Steve called it, the angle bisector theorem
    In this case:
    KL/KN = LM/MN

    11/(x-4) = (2x+1.3)/5.4
    2x^2 - 6.7x - 5.2 = 59.4
    2x^2 - 6.7x - 64.6 = 0
    20x^2 - 67x - 646 = 0
    x = (67 ± √56169)/40

    = 7.6 or a negative which will not work in 2x+1.3

    KN = x-4 = 7.6 - 4 = 3.6
    LM = 2x+1.3 = 15.2 + 1.3 = 16.5

    check:
    LK/KN = 11/3.6 = 55/18
    LM/MN = 16.5/5.4 = 55/18

  • Geometry-8th gr - ,

    Thanks.

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