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UPSC 2014 CDS I Math Paper
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© examsnet.com
Question : 80
Total: 100
Let ABCD be a parallelogram . Let P, Q, R, S be the mid-points of sides AB, BC, CD, DA respectively. Consider th e following statements:
1. Area of triangle APS < Area of triangle DSR if BD < AC.
2. Area of triangle ABC = 4 (Area of triangle BPQ).
elect the correctansw er using the code given below :
[2014 CDS-I]
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Validate
Solution:
BD < AC
∴
1
2
B
D
<
1
2
A
C
⇒
S
P
<
S
R
In ΔAPS and ΔDSR
AS = DS, AP = DR but SP < SR
∴ ar ΔAPD < ar ΔDSR
Thus statement 1 is correct
In ΔBPQ and ΔABC
Thus statement 2 is correct.
ar
Δ
BPQ
ar
Δ
ABC
=
(
PQ
AC
)
2
=
(
1
2
)
2
=
1
4
⇒
Δ
ABC
=
4
Δ
BPQ
© examsnet.com
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