jmc

Because $△PQR$ is isosceles with $PQ=QR$, median $\overline{QM}$ is also an altitude:



We have $MP=PR/2=16$, so right triangle $PQM$ gives us $$\begin{array}{rl}QM& =\sqrt{P{Q}^2-P{M}^2}\\ & =\sqrt{34^2-16^2}\\ & =\sqrt{(34-16)(34+16)}\\ & =\boxed{30}.\end{array}$$ (We might also have recognized that $PM/PQ=8/17$, so $QM/PQ=15/17$.)