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UPSC CDS Math Triangles Questions
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© examsnet.com
Question : 52
Total: 68
Two poles are placed at P and Q on either side of a road such that the line joining P and Q is perpendicular to the length of the road. A person moves x metre away from P parallel to the road and places another pole at R. Then the person moves further x metre in the same direction and turns and moves a distance y metre away from the road perpendicularly, where he finds himself, Q and R on the same line. The distance between P and Q (i.e., the width of the road) in metre is
[2016 CDS-I]
x
x
2
y
2
y
Validate
Solution:
In ΔPRQ and ΔSRT,
∠PRQ = ∠SRT (Vertically opposite angles)
∠QPR = ∠TSR (90°)
∴ ΔPRQ ~ ΔSRT (AA similarity)
⇒
P
Q
S
T
=
P
R
S
R
(Corresponding sides are proportional)
⇒
P
Q
y
=
x
x
⇒
P
Q
=
y
m
© examsnet.com
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