# Thread: Explain how to solve this triangle question?

1. ## 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

2. ## Re: Explain how to solve this triangle question?

Originally Posted by Ilikebugs
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 $\overline{AC}=\sqrt{4x^2+4y^2}$.