CEMC Banner

Problem of the Week
Problem E
Medians

In \(\triangle ABC\), \(\angle ABC = 90^{\circ}\). A median is drawn from \(A\) to side \(BC\), meeting \(BC\) at \(M\) such that \(AM=5\). A second median is drawn from \(C\) to side \(AB\), meeting \(AB\) at \(N\) such that \(CN=2\sqrt{10}\).

Determine the length of the longest side of \(\triangle ABC\).

Note: In a triangle, a median is a line segment drawn from a vertex of the triangle to the midpoint of the opposite side.