If $\Delta PQR \sim \Delta XYZ$ under the correspondence $PQR \leftrightarrow XYZ$,and given that $3 QR = 4 YZ$ and $PR = 8$,find the length of $XZ$.

$\Delta DEF \sim \Delta PQR$ for the correspondence $DEF \leftrightarrow QPR$. If $2 DE = 3 PQ$ and $QR = 8$,then $DF = \ldots$

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AM = 12$ and $CM = 3$,find $BM$.

If $\Delta ABC \sim \Delta PQR$ under the correspondence $ABC \leftrightarrow PQR$. If $AB = 12$,$\text{Area}(\Delta ABC) = 36$,and $\text{Area}(\Delta PQR) = 64$,then $PQ = \ldots$

For $\Delta ABC$ and $\Delta XYZ$,$\frac{AB}{XZ} = \frac{BC}{XY} = \frac{AC}{YZ}$. Then,the correspondence $ABC \leftrightarrow \ldots \ldots$ between them is a similarity.

If in two triangles $ABC$ and $PQR$,$\frac{AB}{QR} = \frac{BC}{PR} = \frac{CA}{PQ}$,then