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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
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B
20 cm
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C
15 cm
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D
30 cm
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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 $$ABCD = 20cm$$.

822603_569227_ans_52e5c0bd3aa240dba57cbd05f0a11de1.jpeg

Mathematics

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