2016 · Q50
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
Elementary MathematicsGeometry: Lines, Angles and Triangles
- Ax
- Bx/2
- Cy
- D2y
Explanation
Place P = (0,0), Q = (0,w), R = (x,0) and the final point S = (2x,−y). Collinearity of Q, R, S gives (−y−0)/(2x−x) = (w−0)/(0−x), i.e. −y/x = −w/x, so w = y. The road width is y, option C.