Find the length of the longest rod that can be placed in a room 10 m long, 8 m wide and 6 m high.

The longest edge of a cuboid is the body diagonal

So the length of longest rod will be same as the length of body diagonal

Length of room = l = 10 m

Breadth of room = b = 8 m

Height of room = h = 6 m

Length of body diagonal =

⇒ length of rod =

=

=

Therefore, length of longest rod = 10√2 m