In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is a median. If $AC = 20$,then $BM = \ldots$

In $\Delta ABC$,$m \angle A = 90^{\circ}$ and $\overline{AM}$ is an altitude to the hypotenuse $\overline{BC}$. If $BM = 6$ and $CM = 2$,find the perimeter of $\Delta ABC$.

As shown in the adjoining diagram of a staircase,the width of each step is $20 \, cm$ and the height is $15 \, cm$. Find the distance between points $A$ and $B$ in meters.

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QD}$ is an altitude to the hypotenuse $\overline{PR}$. If $PQ = 4QR$,prove that $PD = 16RD$.

$A$ $6.5 \, m$ long ladder leans on a wall to reach a height of $6 \, m$ on the wall. Then,the lower end of the ladder remains $\ldots \ldots \ldots \ldots \, m$ away from the wall.

It is given that $\triangle ABC \sim \triangle DFE$,$\angle A = 30^{\circ}$,$\angle C = 50^{\circ}$,$AB = 5 \, cm$,$AC = 8 \, cm$ and $DF = 7.5 \, cm$. Then,the following is true: