In $\Delta ABC$,$\overline{AD}$ is a median. If $AB = 10$,$BC = 16$ and $AD = \sqrt{58}$,find $AC$.

The length of a ladder is $6 \,m$ and it leans on a wall to reach the height of $3.6 \,m$. Find the distance in $m$ between the lower end of the ladder and the base of the wall.

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AM = 12$ and $CM = 3$,then $BM = \dots$

Transversals $t_{1}$ and $t_{2}$ to $l_{1} \parallel l_{2} \parallel l_{3}$ intersect them at $A, B, C$ and $P, Q, R$ respectively. If $AB = 3, BC = 4$ and $QR = 3.6$,find $PR$.

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $BD = 2.5$,$AB = 5$ and $AC = 4.2$,find $DC$.

$\Delta XYZ \sim \Delta DEF$ for the correspondence $XYZ \leftrightarrow EFD$. If $XY : EF = 2 : 3$ and the area of $\Delta XYZ$ is $18$,then the area of $\Delta DEF$ is........