Question

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

A
10 cm
B
20 cm
C
15 cm
D
30 cm

Solution

## The correct option is C $$20\ cm$$$$\Rightarrow$$   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 $$ABCD = 20cm$$.Mathematics

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