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

In rhombus $XYZW$,$XZ = 14$ and $YW = 48$. Then,$XY = \ldots \ldots \ldots$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BD}$ is a median. If $AB = 5$ and $BC = 12$,find $BD$.

$A$ flag pole $18 \, m$ high casts a shadow $9.6 \, m$ long. Find the distance of the top of the pole from the far end of the shadow. (in $m$)

In $\Delta ABC$,$m \angle A = m \angle B + m \angle C$. If $AB = 7$ and $BC = 25$,the perimeter of $\Delta ABC = ........$

In quadrilateral $ABCD$,$P$ is the midpoint of $\overline{BC}$. If $\overline{DP}$ produced intersects $\overline{AB}$ produced at $Q$,prove that $AB = 2CD$ given that $ABCD$ is a parallelogram.