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

In $\Delta PQR$,$m \angle P = 90^{\circ}$ and $\overline{PM}$ is an altitude. If $QM = 2x^{2}$ and $RM = 8x^{2}$,then $PM = \ldots \ldots$

In $\Delta ABC$,$AB = 17$,$BC = 15$,and $AC = 8$. Then,the length of the median on the longest side of the triangle is $\ldots$.

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AC = 25$ and $AM = 16$,then $BM = \dots$

In rhombus $XYZW$,$XZ = 14$ and $YW = 48$. Then,$XY = \ldots \ldots \ldots$.

In the figure,$ABC$ is a triangle right-angled at $B$ and $BD \perp AC$. If $AD = 4 \, cm$ and $CD = 5 \, cm$,find $BD$ and $AB$.