The lengths of the diagonals of a rhombus are $16 \, cm$ and $12 \, cm$. Then,the length of the side of the rhombus is (in $cm$)

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM : AB = 2 : 3$ and $AC = 15$,then $NC = \ldots$

In $\Delta XYZ$,$\overline{XM}$ is a median. If $XY = 11$ and $XM = YM = 30.5$,find $XZ$.

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 5.2$,$AC = 10.4$,and $BD = 3.8$,find $BC$.

$A$ $6.5 \, m$ 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.

$A$ $17 \, m$ long ladder leans on a wall such that its lower end rests $8 \, m$ away from the base of the wall. Then,its upper end reaches to the height of $\ldots \ldots \ldots \, m$ on the wall.