If $\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow PQR$,$2 AB = PQ$,and $BC = 10$,then $QR = \dots$

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BD}$ is an altitude to the hypotenuse $\overline{AC}$. Then,the correspondence $ABC \leftrightarrow \ldots$ between $\Delta ABC$ and $\Delta ADB$ is a similarity.

$\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow PQR.$ The perimeter of $\Delta ABC$ is $16$ and the perimeter of $\Delta PQR$ is $24.$ If $AB = 6$,find $PQ$.

The length of a diagonal of a square is $8 \sqrt{2}$. Then,its area is $\ldots \ldots \ldots$

In $\Delta XYZ$,$X-S-Y$,$X-T-Z$ and $\overline{ST} \parallel \overline{YZ}$. If $XS = 4$,$XT = 8$,$SY = x-4$ and $TZ = 3x-19$,find the value of $x$.

In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle R$ and $\angle B \cong \angle P$. If $AB = 6$,$BC = 8$ and $PR = 9$,then $PQ = \ldots$