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Question : 52 of 68

Marks: +1, -0

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

$x$
$\frac{x}{2}$
$y$
$2y$

Solution:

In ΔPRQ and ΔSRT,

∠PRQ = ∠SRT (Vertically opposite angles)

∠QPR = ∠TSR (90°)

∴ ΔPRQ ~ ΔSRT (AA similarity)

\Rightarrow\frac{PQ}{ST}=\frac{PR}{SR}

(Corresponding sides are proportional)

\Rightarrow\frac{PQ}{y}=\frac{x}{x}\Rightarrow PQ=y\;\;m

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