Area of the floor of a cubical room is 64 m². The length of the longest rod that can be kept in the room is :

$8\sqrt{3}$ m

We know that,

Area of a floor = side²

The diagonal of a floor = a\(\sqrt {3}\)

Area of the floor of a cubical room = 64 m².

a² = 64

= a = 8 m

The length of the longest rod = 8 × \(\sqrt {3}\)= 8\(\sqrt {3}\) m.