# The length of the longest rod that can be placed in a room of dimensions

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

$=\sqrt{l^{2}+b^{2}+h^{2}}$

$=\sqrt{100+100+25} \mathrm{~m}$

$=\sqrt{225} \mathrm{~m}$

$=15 \mathrm{~m}$