In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AB = 10.8$,$MB = 4.5$ and $AC = 4.8$,find $AN$.

$\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow XYZ$. If $PQ : QR : PR = 3 : 5 : 7$ and the perimeter of $\Delta XYZ$ is $22.5$,then $YZ = \ldots$

In the given figure,if $PQRS$ is a parallelogram and $AB \parallel PS$,then prove that $OC \parallel SR$.

In a rectangle $ABCD$,if $AB^{2} + BC^{2} = 64$,then find the length of the diagonal $AC$.

The length of a diagonal of a square is $8 \sqrt{2}$. Then,its area is $\ldots \ldots \ldots$

$\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow PQR.$ The perimeter of $\Delta ABC$ is $16$ and the perimeter of $\Delta PQR$ is $24.$ If $AB = 6$,find $PQ$.