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UPSC 2015 CDS I Math Paper
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© examsnet.com
Question : 60
Total: 100
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
[2015 CDS-I]
7 : 3
√
7
:
√
3
7 : 5
None of the above
Validate
Solution:
Let AB = 2x and AD = x.
Suppose ∠BAD = 60°
∴ ∠ABC = 180°- 60° = 120° (Pair of alternate interior angles is supplementary)
In ΔABD
B
D
2
=
A
B
2
+
A
D
2
−
2
×
A
B
×
A
D
cos
60
°
=
4
x
2
+
x
2
−
2
×
2
x
×
x
×
1
2
=
3
x
2
⇒
B
D
=
√
3
x
In ΔABC,
A
C
2
=
A
B
2
+
B
C
2
−
2
×
A
B
×
B
C
cos
120
°
=
4
x
2
+
x
2
−
2
×
2
x
×
x
×
(
−
1
2
)
=
7
x
2
⇒
A
C
=
√
7
x
Therefore, ratio of the diagonals
=
A
C
:
B
D
=
√
7
:
√
3
© examsnet.com
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