In rectangle $ABCD$,$AB = 2.4$ and $BC = 3.2$. Then,$AC = \ldots$

Prove that in a parallelogram,the sum of squares of all the sides is equal to the sum of squares of the diagonals.

In $\Delta ABC$,$A-P-B$,$A-Q-C$ and $\overleftrightarrow{PQ} \parallel \overleftrightarrow{BC}$. If $AP = 3$,$PB = 5$ and $AQ = 6$,find $QC$ and $AC$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $D$ is a point on $\overline{BC}$. Prove that $AD^{2} + BC^{2} = AC^{2} + BD^{2}$.

$\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow RPQ$. If $m \angle A + m \angle C = m \angle B$,then in $\Delta PQR$,$\ldots \ldots \ldots$ is a right angle.

$\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow PQR$. If $AB : PQ = 3 : 4$ and the perimeter of $\Delta PQR$ is $24$,find the perimeter of $\Delta ABC$.