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The adjacent sides of a parallelogram are 2a and a. If the angle between them is 60°, then one of the diagonals of the parallelogram is

(a) 3a 

(b) √5a 

(c) 2a 

(d) √3a

1 Answer

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Best answer

(d) √3a

In ∆DAE, 

cos 60° = \(\frac{AE}{a}\), sin 60° = \(\frac{DE}{a}\)

⇒ AE = \(\frac{1}{2}\)a, DE = \(\frac{\sqrt3}{2}\)

∴ BE = BA – AE 

= 2a – \(\frac{1}{2}\)a = \(\frac{3a}{2}\)

∴ In right angled ∆BDE,

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