Longest pole across a rectangular room (space diagonal): A room measures 12 m (length) × 9 m (width) × 8 m (height). Find the length of the longest pole that can fit inside.

Introduction / Context:The longest stick that fits in a rectangular room aligns with the space diagonal of the cuboid. This classic 3D Pythagoras application appears often in aptitude tests.

Given Data / Assumptions:

• L = 12 m, W = 9 m, H = 8 m
• Space diagonal d = √(L^2 + W^2 + H^2)

Concept / Approach:Apply the 3D extension of Pythagoras: d = √(a^2 + b^2 + c^2) for a cuboid with edges a, b, c.

Step-by-Step Solution:d = √(12^2 + 9^2 + 8^2) = √(144 + 81 + 64)d = √289 = 17 m

Verification / Alternative check:Compute floor diagonal first: √(12^2 + 9^2) = √225 = 15; then √(15^2 + 8^2) = √(225 + 64) = √289 = 17. Same result.

Why Other Options Are Wrong:12 m and 14 m are below the space diagonal; 21 m exceeds any dimension; 15 m is only the floor diagonal, not the space diagonal.

Common Pitfalls:Using only the floor diagonal; mixing up dimensions; arithmetic errors when squaring and adding.

Final Answer:17 m