Question

Find the length of the longest rod that can be placed in a room 12 m long, 9 m broad and 8 m high

Answer 1

longest rod placed in a room = it's diagonal
=
$\sqrt{12 \times 9 \times 8}$
$\sqrt{9 \times 96}$
$3 \sqrt{96}$
$3 \sqrt{16 \times 6}$
$3 \times 4 \sqrt{6}$
$12 \sqrt{6} \: cm$

Answer 2

therefore the longest rod that can be placed in the room is of length 17 m .
hope you understand