In rhombus $ABCD$,$AC = 15$ and $BD = 36$. Find the perimeter of rhombus $ABCD$.

In $\Delta PQR$,$m\angle Q = 90^{\circ}$ and $\overline{QM}$ is an altitude to the hypotenuse $PR$. If $PQ = 8$ and $QR = 6$,find the area of $\Delta QMR$.

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $MA = 6$,$MB = 9$ and $MC = 8$,then $MD = \dots$

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude. If $AM = x + 7$,$BM = x + 2$,and $CM = x$,find the value of $x$.

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QM}$ is an altitude to the hypotenuse $PR$. If $QR = 9$ and $PR = 13.5$,find $RM$.

If $\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow QRP$ and $m \angle A : m \angle B : m \angle C = 2 : 3 : 5$,then $m \angle R = \dots$ (in $^{\circ}$)