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Problem of the Week
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.

In triangle ABC, point D divides BC into two equal segments, BD and DC. Vertex A is located above segment DC.

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