Question:
The length of the longest rod that can be placed in a room of dimensions (10 m × 10 m × 5 m) is
(a) 15 m
(b) 16 m
(c) $10 \sqrt{5} \mathrm{~m}$
(d) 12 m
Solution:
(a) 15 m
Length of longest rod = diagonal of the room
= diagonal of a cuboid
$=\sqrt{l^{2}+b^{2}+h^{2}}$
$=\sqrt{100+100+25} \mathrm{~m}$
$=\sqrt{225} \mathrm{~m}$
$=15 \mathrm{~m}$