In $\Delta ABC$,$\overline{AD}$ is a median. If $AB = 10$,$AC = 24$,and $AD = 13$,find $BC$.

$\Delta XYZ \sim \Delta DEF$ 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........

In $\Delta ABC$ and $\Delta XYZ$,$m\angle A = m\angle X$,$m\angle B = m\angle Y$ and $\frac{AB}{XY} = \frac{2}{3}$. If $AC = 7.2$,then $XZ = \ldots$

$D$ is a point on side $QR$ of $\triangle PQR$ such that $PD \perp QR$. Will it be correct to say that $\triangle PQD \sim \triangle RPD$? Why?

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 $\Delta ABC$.

If $\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow ZYX$,and given $PQ = 6$,$QR = 8$,and $XY = 12$,find the length of $YZ$.