Two walls and a ceiling of a room meet at right angles at a point P. A fly is in the air 1 m from one wall, 8 m from the other wall and 9 m from the point P. How many meters is the fly from the ceiling?
- (a) 4 ✓ UPSC's answer
- (b) 6
- (c) 12
- (d) 15
Why the answer is (a)
• Take P as the corner. The fly's distances from the two walls and the ceiling are its three perpendicular coordinates, and its distance from P is the length of the diagonal.
• So 1² + 8² + h² = 9², that is 1 + 64 + h² = 81, giving h² = 16 and h = 4.
• The fly is 4 m from the ceiling, option (a).
Why the other options are wrong
- (b) 6
- 1² + 8² + 6² = 101, not 9² = 81.
- (c) 12
- 1² + 8² + 12² = 209, not 81.
- (d) 15
- 1² + 8² + 15² = 290, not 81.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.