In square $ABCD$,$AB = 4 \sqrt{2}$. Then,the length of a diagonal of the square is......

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

In $\Delta PQR$,the bisector of $\angle P$ intersects $\overline{QR}$ at $S$. If $PQ = 15$,$QS = 10$,and $SR = 8$,then $PR = $.........

If $\Delta PQR \sim \Delta XYZ$ under the correspondence $PQR \leftrightarrow XYZ$,and given that $3 QR = 4 YZ$ and $PR = 8$,find the length of $XZ$.

In $\Delta ABC$,$m\angle B = 90^{\circ}$. If $a = 16$ and $c = 12$,then $b = \ldots$

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.