Question

In the above figure, the area of parallelogram $PQRS$ is $24$ and $QR=6$. If $\overline{QT}$ is perpendicular to $\overline{PS}$ and if $T$ is the midpoint of $\overline{PS}$, calculate the perimeter of $PQRS$.

• A. $20$
• B. $22$
• C. $24$
• D. $26$$
• E. 28

Answer 1

The correct option is B $22$

Area of parallelogram is $24=QT\times QR=QT\times 6$, which gives $QT=4$
$T$ is midpoint, so $PT=TS=3$

So, $PQ=\sqrt{3^2+4^2}$

$=\sqrt{16+9}$

$=\sqrt{25}$

$=5$
Perimeter of parallelogram is $QR+RS+SP+PQ=6+5+6+5=22$.