In rectangle $ABCD$,$AB = 9$ and $BC = 12$. Then,$BD = \ldots$

Below are given the measures of sides $\overline{PQ}$,$\overline{QR}$ and $\overline{PR}$ of $\Delta PQR$. In each case,determine whether $\Delta PQR$ is a right-angled triangle or not. If it is a right-angled triangle,state which angle is a right angle: $PQ = 7, QR = 24, PR = 25$.

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $BD = 2.5$,$AB = 5$ and $AC = 4.2$,find $DC$.

$\Delta ABC \sim \Delta DEF$ for the correspondence $ABC \leftrightarrow DEF$. If $3 AB = 5 DE$ and $DF = 9$,then $AC = \ldots$

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

In $\Delta ABC$ and $\Delta PQR$,$m \angle A = m \angle R$ and $m \angle B = m \angle Q$. Then,the correspondence $ABC \leftrightarrow \ldots$ is a similarity.