# Problem of the Week Problem D Which Term is Which?

In $$\triangle PQR$$, $$\angle PRQ = 90^{\circ}$$. An altitude is drawn in $$\triangle PQR$$ from $$R$$ to $$PQ$$, intersecting $$PQ$$ at $$S$$. A median is drawn in $$\triangle PSR$$ from $$P$$ to $$SR$$, intersecting $$SR$$ at $$T$$.

If the length of the median $$PT$$ is $$39$$ and the length of $$PS$$ is $$36$$, determine the length of $$QS$$.

Note: An altitude of a triangle is a line segment drawn from a vertex of the triangle perpendicular to the opposite side. A median is a line segment drawn from a vertex of the triangle to the midpoint of the opposite side.