In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QM}$ is an altitude. If $QM = 6$ and $MR = 9$,then $PR = \ldots$

$\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow YZX$. If $m \angle P = 2 m \angle Q$ and $m \angle X = 120^\circ$,then $m \angle Y = \dots$ (in $^\circ$)

In a rectangle $ABCD$,if $AB + BC = 47$ and the diagonal $AC = 37$,find the lengths of $AB$ and $BC$,given that $AB > BC$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude. If $AB = \sqrt{10}$ and $AM = 2.5$,then $MC = \ldots$

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB : AC = 3 : 4$ and $BC = 14$,find $BD$.

In $\Delta XYZ$,$P$ and $Q$ are the midpoints of $\overline{XY}$ and $\overline{XZ}$ respectively. If the area of $\Delta XYZ$ is $140$,find the area of $\Delta XPQ$.