A hall is 12 m long, 9 m wide and 8 m high. What is the length, in metres, of the longest straight rod that can be placed inside it?

The longest rod lies along the space diagonal of the cuboid: √$(l^2+b^2+h^2)$ = √$(144+81+64)$ = √289 = 17 m. The trap 15 is √(144 + 81), the diagonal of the FLOOR only, with the height ignored; 289 is the sum of the squares with the square root never taken; 29 simply adds 12 + 9 + 8.