Question

Construct a parallelogram $ABCD$, with $AB=6cm,BC=4cm$ and $\angle ABC={60}^{\circ }$. Then the perimeter of the parallelogram is:

• A. $10cm$
• B. $20cm$
• C. $15cm$
• D. $30cm$

Answer 1

Answer: (B)

$20cm$

$\Rightarrow$ Draw a line segment AB = 6cm.

$\Rightarrow$ Construct an angle of ${60}^{\circ }$ at point B.

$\Rightarrow$ Cut off BC = 4cm.

$\Rightarrow$ We know that adjacent angles of parallelogram are supplementary then, construct an angle of ${120}^{\circ }$ at point A and C which meet at point D.

$\Rightarrow$ Thus, $ABCD$ is a required parallelogram.

$\Rightarrow$ Let $AB=a=6cm$ and $BC=b=4cm$ --- ( 1 )

$\Rightarrow$ Perimeter of parallelogram $ABCD=2(a+b)$

$\Rightarrow$ $2(6+4)$ [From( 1 )]

$\therefore$ Perimeter of parallelogram $ABCD=20cm$.