Problem D

There are Two Sides

A *median* is a line segment drawn from the vertex of a triangle to the midpoint of the opposite side.

In \(\triangle ABC\), a median is drawn from vertex \(A\), meeting side \(BC\) at point \(D\). The length of \(BD\) is \(6\) cm and the length of the median \(AD\) is \(13\) cm.

The area of \(\triangle ABC\) is \(72 \text{cm}^2\). Determine the lengths of sides \(AB\) and \(AC\).