2026 · Q76
A room is L m long, B m wide and H m high. Further, L > B > H and L, B and H are integers. The length of the longest pole that can be placed in the room is 17 m and the length of the longest pole that can be placed on the floor is 15 m. What is the volume of the room?
Elementary MathematicsMensuration
- A432 m³
- B864 m³
- C1296 m³
- DCannot be determined due to insufficient data
Explanation
The floor diagonal gives L² + B² = 225 and the space diagonal gives L² + B² + H² = 289, so H² = 64 and H = 8. With L > B > 8 integers and L² + B² = 225, the only solution is L = 12, B = 9. The volume is 12 × 9 × 8 = 864 m³, option B.