If $\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow PQR$. If $AB = 5, BC = 7, AC = 10$ and $PR = 15$,the perimeter of $\Delta PQR$ is........

In $\Delta PQR$,$m \angle P = m \angle Q + m \angle R$,$PQ = 7$ and $QR = 25$. Find the perimeter of $\Delta PQR$.

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 12$,$AC = 8$ and $BD = 9$,find $DC$.

If $\Delta XYZ \sim \Delta DEF$ for the correspondence $XYZ \leftrightarrow EFD$.
If $m \angle X : m \angle Y : m \angle Z = 2 : 3 : 5$,then in $\Delta DEF$,$\ldots \ldots$ is a right angle.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BD}$ is an altitude to the hypotenuse $AC$. If $AD = 9$ and $CD = 27$,find $AB$.

In $\Delta PQR$,the bisector of $\angle P$ intersects $\overline{QR}$ at $S$. If $PQ : PR = 5 : 4$ and $SR = 5.6 \text{ cm}$,then $QR = \ldots \text{ cm}$.