The lengths of the diagonals of a rhombus are $10$ and $24$. Then,the length of each side of the rhombus is $\ldots \ldots \ldots \ldots . .$

The perimeter of square $ABCD$ is $20$. Find $AC$. (in $\sqrt{2}$)

In $\Delta ABC$ and $\Delta PQR$,$m \angle A = 30^{\circ}$,$m \angle C = 60^{\circ}$,$m \angle P = 90^{\circ}$ and $m \angle Q = 30^{\circ}$. Then,the correspondence $ABC \leftrightarrow \ldots$ is a similarity.

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 $\Delta PQR$,$\angle P$ is a right angle and $\overline{PX}$ is an altitude. If $QX = 4$ and $RX = 5$,then $PQ = \ldots \ldots$

In $\Delta ABC$,$\overline{AD}$ is a median. If $AB = 8$,$BC = 18$,and $AD = 7$,then $AC = \ldots$