In $\Delta ABC$,$m\angle B = 90^{\circ}$. If $a = 16$ and $c = 12$,then $b = \ldots$

In $\Delta ABC$,$\Delta PQR$,and $\Delta XYZ$,the correspondences $ABC \leftrightarrow QPR$ and $PQR \leftrightarrow YZX$ are similarities. Then,the correspondence $ABC \leftrightarrow \dots$ is a similarity.

In $\Delta PQR$,$m \angle Q : m \angle R : m \angle P = 1 : 2 : 1$. If $PQ = 2 \sqrt{6}$,then $PR = \ldots$

In $\Delta ABC$ and $\Delta XYZ$,$m \angle A = m \angle X$ and $m \angle B = m \angle Y$. $\overline{AM}$ is a median of $\Delta ABC$ and $\overline{XP}$ is a median of $\Delta XYZ$. Prove that $AM \times YZ = XP \times BC$.

Find the altitude of an equilateral triangle of side $8 \, cm$. (in $cm$)

If $\Delta ABC \sim \Delta XYZ$ for the correspondence $ABC \leftrightarrow XYZ$,and $\frac{AB}{4} = \frac{XY}{5}$,then $\frac{BC}{YZ} = \ldots$