In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $\frac{AM}{MB} = \frac{2}{3}$ and $AC = 25$,find $NC$.

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 $XZ = \ldots$

If $\Delta ABC \sim \Delta MNP$ for the correspondence $ABC \leftrightarrow MNP,$ the perimeter of $\Delta ABC$ is $18$ and the perimeter of $\Delta MNP$ is $27.$ If $AB = 8,$ then $MN = \dots$

$\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow QPR.$ If $m \angle P : m \angle Q : m \angle R = 2 : 3 : 4,$ then $m \angle A : m \angle B : m \angle C = \ldots$

In $\Delta XYZ$,$m\angle Y = 90^{\circ}$ and $\overline{YM}$ is an altitude to the hypotenuse $\overline{XZ}$. If $YM = 12$ and $XM = 8$,find $XZ$.

$\Delta ABC \sim \Delta DEF$ for the correspondence $ABC \leftrightarrow EFD$. $AB : BC : CA = 4 : 3 : 5$. If the perimeter of $\Delta DEF$ is $36$,find the measures of all the sides of $\Delta DEF$.