$ABCD$ is a parallelogram with $\angle ABC={60}^{\mathrm{o}}$. If the longer diagonal is of length $7 cm$ and the area of the parallelogram $ABCD$ is $15 \frac{\sqrt{3}}{2} c{m}^2$, then the perimeter of the parallelogram (in $cm$) is:

A city has a park shaped as a right angled triangle. The length of the longest side of this park is $80 m$. The Mayor of the city wants to construct three paths from the corner point opposite to the longest side such that these three paths divide the longest side into four equal segments. Determine the sum of the squares of the lengths of the three paths (in $m^2$)

In a rectangle $PQRS,PQ=14 cm$, $X$ is a point on $SR$ such that $SX:XR=4:3$ and $QX=10 cm$. If $\angle PXQ=a,\angle XPQ=b,\angle XQP=c$, then which of the fol lowing is correct?