In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $AC$. If $AM = 7$ and $CM = 9$,then $BC = \ldots$.

$A$ $17 \, m$ long ladder leans on a wall such that its lower end rests $8 \, m$ away from the base of the wall. Then,its upper end reaches to the height of $\ldots \ldots \ldots \, m$ on the wall.

In $\Delta PQR$,$\angle P$ is a right angle and $\overline{PX}$ is an altitude. If $QX = 4$ and $RX = 5$,then $PQ = \ldots \ldots$

The ratio of the corresponding sides of two similar triangles is $4:9$. Then,the ratio of their areas is $\ldots \ldots$.

Legs (sides other than the hypotenuse) of a right triangle are of lengths $16 \,cm$ and $8 \,cm$. Find the length of the side of the largest square that can be inscribed in the triangle. (in $cm$)

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