In $\Delta ABC$,$D$ is the midpoint of $\overline{BC}$,$AB = 7$,$AC = 5$ and $AD = 5$. Then $BC = \ldots$

In rhombus $XYZW$,$XZ = 14$ and $YW = 48$. Then,$XY = \ldots \ldots \ldots$.

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QM}$ is an altitude to the hypotenuse $\overline{PR}$. If $QM = 4$ and $PR = 10$,find $PM$.

The correspondence $ABC \leftrightarrow QPR$ between $\Delta ABC$ and $\Delta PQR$ is a similarity. If $m \angle A : m \angle B : m \angle C = 15 : 8 : 7$,find the measures of all the angles of $\Delta PQR$.

In $\Delta ABC$,$A-P-B$,$A-Q-C$ and $\overline{PQ} \parallel \overline{BC}$. If $AP = 8x-7$,$PB = 5x-3$,$AQ = 4x-3$ and $QC = 3x-1$,find the value of $x$.

In $\Delta XYZ$,$X-P-Y$,$X-Q-Z$ and $\overline{PQ} \parallel \overline{YZ}$. If $XY = 5.6$,$XP = 1.4$ and $XZ = 7.2$,find $XQ$.