In $\Delta ABC$,$m \angle B = 90^{\circ}$. If $AB = 4$ and $BC = 7.5$,find $AC$.

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $AC$. If $BM = \sqrt{30}$ and $CM = 3$,find $AC$.

$\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow XYZ$. The perimeter of $\Delta PQR$ is $24$ and the perimeter of $\Delta XYZ$ is $60$. If $PR = 10$,find $XZ$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude. If $BM = 12$ and $AM = 9$,then $AC = \ldots$

In $\Delta ABC$, $P$ and $Q$ are the midpoints of $\overline{AB}$ and $\overline{AC}$ respectively. If the area of $\Delta APQ = 12 \sqrt{3}$, then the area of $\Delta ABC = \ldots$ (in $\sqrt{3}$)

$\Delta XYZ \sim \Delta ABC$ for the correspondence $XYZ \leftrightarrow ABC$. If $\frac{XY}{AB} = \frac{3}{5}$,then $\frac{BC}{YZ} = \dots$