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Thread: Explain how to solve this triangle question?

  1. #1
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    Explain how to solve this triangle question?

    In triangle ABC, ∠ABC = 90◦
    . A median is drawn from A meeting BC at M such
    that AM = 5. A second median is drawn from C meeting AB at N such that
    CN = 2√10.
    Determine the length of the longest side of triangle ABC
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  2. #2
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    Re: Explain how to solve this triangle question?

    Quote Originally Posted by Ilikebugs View Post
    In triangle ABC, ∠ABC = 90◦
    . A median is drawn from A meeting BC at M such
    that AM = 5. A second median is drawn from C meeting AB at N such that
    CN = 2√10.
    Determine the length of the longest side of triangle ABC
    Label the length of $\overline{BN}=x$ and the length of $\overline{BM}=y$. From this we get
    $4x^2+y^2=25\\x^2+4y^2=40$
    Solve those for $x~\&~y$ Then the the length of $\overline{AC}=\sqrt{4x^2+4y^2}$.
    Last edited by Plato; Sep 24th 2016 at 03:44 PM.
    Thanks from topsquark
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