ABCD is a parallelogram where AB AD 2 1 One of the angles of the parallelogram is 60 deg The two dia...........

Quantitative Aptitude (CDS) Mensuration 2D

ABCD is a parallelogram, where AB : AD = 2 : 1. One of the angles of the parallelogram is 60°. The two diagonals are in the ratio

7 : 3

√7 : √3

7 : 5

None of the above

Let AB = 2x and AD = x.
Suppose ∠BAD = 60°
∴ ∠ABC = 180°- 60° = 120° (Pair of alternate interior angles is supplementary)
In ΔABD

BD²=AB²+AD²−2×AB×AD cos60°

=4x2+x2−2×2x×x×1/2=3x²
⇒BD=√3x
In ΔABC,

AC²=AB²+BC²−2×AB×BC cos120°
=4x²+x²−2×2x×x×(−1/2)=7x²
⇒AC=√7x
Therefore, ratio of the diagonals=AC:BD=√7:√3

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