Question

Construct a parallelogram $PQRS$, given $PQ=5$ cm, $QR=4$ cm and $\angle PQR={70}^o$ and calculate the perimeter of the parallelogram.

• A. $12$ cm
• B. $18$ cm
• C. $16$ cm
• D. None of these

Answer 1

The correct option is B $18$ cm

$\Rightarrow$ We know that opposite sides and angle of parallelogram are equal.

$\Rightarrow$ And adjacent angles of parallelogram are supplementary. By using these properties we are going to construct a parallelogram.

$\Rightarrow$ Draw a line segment $PQ=5cm$

$\Rightarrow$ Construct an angle of ${70}^{\circ }$ at point $Q$.

$\Rightarrow$ Cut off $QR=4cm$

$\Rightarrow$ Construct an angle of ${110}^{\circ }$ at point $P$.

$\Rightarrow$ Cut off $PS=4cm$

$\Rightarrow$ Join $RS$

$\Rightarrow$ Thus $PQRS$ is a required parallelogram

$\Rightarrow$ Let $a=5cm$ and $b=4cm$

$\Rightarrow$ Perimeter of parallelogram $PQRS=2(a+b)$ $=2(5+4)=18$

$\Rightarrow$ The perimeter of parallelogram $PQRS=18cm$