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

Answer : Option C

Explanation :

In $\Delta \mathrm{PQR}$ and $\Delta \mathrm{RST}$

In $\Delta \mathrm{PQR}$ and $\Delta \mathrm{RST}$

$\angle \mathrm{TRS}=\angle \mathrm{PRQ}$

$\angle \mathrm{TSR}=\angle \mathrm{RPQ}=90^{\circ}$

By A A - similarity,

$\Delta \mathrm{PQR} \cong \Delta \mathrm{RST}$

$\therefore \frac{\mathrm{RS}}{\mathrm{ST}}=\frac{\mathrm{PR}}{\mathrm{PQ}}$ $\Rightarrow \frac{x}{y}=\frac{x}{\mathrm{PQ}} \Rightarrow \mathrm{PQ}=y$ metre