In parallelogram $ABCD$,the diagonals intersect at $P$. If $PA = 3.8 \, cm$ and $PB = 5.2 \, cm$,then $BD = \dots \dots \dots cm$.

In $\Delta ABC$,$P$,$Q$,and $R$ are the midpoints of $AB$,$BC$,and $AC$ respectively. If $AB = 8 \text{ cm}$,$BC = 9 \text{ cm}$,and $AC = 10.6 \text{ cm}$,find the perimeter of $\Delta PQR$ in $\text{cm}$.

Perimeter of rectangle $PQRS$ is $40\, cm$. If $PQ : QR = 3 : 5$,then $RS = \ldots \ldots \ldots \, cm$.

$E$ and $F$ are points on diagonal $AC$ of a parallelogram $ABCD$ such that $AE = CF$. Show that $BFDE$ is a parallelogram.

In $\Delta ABC$,$P, Q,$ and $R$ are the midpoints of $AB, BC,$ and $CA$ respectively. Prove that $PBQR, PQCR,$ and $PQRA$ all are parallelograms.

Can all the angles of a quadrilateral be right angles? Give reason for your answer.