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prashant sharma

· started a discussion

· 1 Months ago

doubtful question (Question: 111644.0 )

if we take diagonal BD then each angle of triangle ABD is 60
it means given figure is a rhombus

Question:
The adjacent sides of a parallelogram are 2a and a. If the angle between sides of parallelogram is 60°, then one of the diagonals of the parallelogram is:
Options:
A) 3a 
B) 2a
C) \(\sqrt[]{7}a\)
D) \(\sqrt[]{5}a\)
Solution:
Ans: (c)


Clearly


\(\angle \)ABC = 120°

From \(\triangle\)CAB,

cos B = \(\cfrac{C^2+a^2-b^2}{2ca}\)

we get

cos (180o- 60o) =\(\cfrac{4a^2+a^2-AC^2}{2\times2a\times a}\)

or \(-\cfrac{1}{2}=\cfrac{5a^2-AC^2}{4a^2}\)

or -2a2 = 5a2 - AC2

or AC2 =7a2

\(\therefore AC =\sqrt{7}a\)

Knowledge Expert

· commented

· 1 Months ago

Dear Student, We have not taken the angle as 90 , please see the image carefully. Angle between the sides is 60 and the angle between side 2a and diagnol is 30. Given answer is right. Thanks and Regards Team TR

GYANENDRA KUMAR

· commented

· 1 Months ago

I agree with you

Abhishek Shah

· commented

· 1 Months ago

also according to their solution angleACB will be 30 ane triangle will be isosceles...How 2a=a ??
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