The perimeter of rectangle $ABCD$ is $112 \, cm$ and $AB : BC = 5 : 3$. Find the length of $AB$ in $cm$.

The angles of a quadrilateral are in the ratio $3:4:6:5$. Find the measure of the greatest angle. (in $^\circ$)

$PQRS$ is a square. If $PR = 10 \, cm$,then the area of $PQRS = \dots \, cm^2$.

Show that in a quadrilateral $ABCD$,$AB + BC + CD + DA < 2(BD + AC)$.

In $\Delta PQR$,$PM$ is a median and $N$ is the midpoint of $PM$. If $\text{ar}(PQN) = 36 \text{ cm}^2$,then $\text{ar}(PQR) = \dots \text{ cm}^2$.

If angles $A, B, C$ and $D$ of the quadrilateral $ABCD$,taken in order,are in the ratio $3:7:6:4$,then $ABCD$ is a