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 $QR = \ldots \text{ cm}$.

In rhombus $ABCD$,$AC = 18$ and $BD = 24$. Find the perimeter of rhombus $ABCD$.

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AM = 12$ and $BM = 12$,find $AC$.

$\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow QRP$. If $m \angle A = 80^{\circ}, m \angle B = 40^{\circ}$ and $m \angle C = 60^{\circ}$,find the measures of all the angles of $\Delta PQR$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is a median. If $AB = 15$ and $BC = 20$,find $BM$.

$\Delta ABC$ and $\Delta PQR$ are equilateral triangles. If $\frac{AB}{PQ} = \frac{3}{2}$,prove that $4 \times \text{Area of } \Delta ABC = 9 \times \text{Area of } \Delta PQR$.