CDS 2025 · PYQ · Mensuration / 3D Geometry · medium
A lamp is kept on a vertical pole. The height of the top of the lamp above the ground is 5√3/2 m. The perpendicular distances of the bottom of the pole from two adjacent walls meeting perpendicularly are 0·7 m and 2·4 m. What is the distance of the top of the lamp from the corner point of the walls on the ground?
A.3 m
B.5 m✓ Correct
C.6 m
D.7 m
Explanation
The corner of the walls is at distance √(0.7² + 2.4²) = √(0.49 + 5.76) = √6.25 = 2.5 m from the foot of the pole on the ground. The height of the lamp top is 5√3/2 m. The distance from corner to top of lamp = √(2.5² + (5√3/2)²) = √(6.25 + 75/4) = √(25/4 + 75/4) = √(100/4) = √25 = 5 m.
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