In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude. If $AB = \sqrt{10}$ and $AM = 2.5$,then $MC = \ldots$

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 $XZ$.

In $\Delta XYZ$,$m\angle X = 90^{\circ}$,$XY = 8$ and $YZ = 17$. Then,the area of $\Delta XYZ$ is.............

In $\Delta XYZ$,the midpoints of the sides are $A, B$ and $C$. In $\Delta ABC$,the midpoints of the sides are $P, Q$ and $R$. If the area of $\Delta ABC$ is $24$,find the area of $\Delta XYZ$ and $\Delta PQR$.

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $\frac{AM}{MB} = \frac{4}{5}$ and $NC = 2.5$,find $AN$.

In $\Delta ABC$,$D$ and $E$ are the midpoints of $\overline{BC}$ and $\overline{AC}$ respectively. $\overline{AD}$ and $\overline{BE}$ intersect at $G$. Line $m$ passing through $D$ and parallel to $\overline{BE}$ intersects $\overline{AC}$ at $K$. Then,$AC = \ldots$ (in $EK$)