Question

Find the length of the longest rod that can be placed in a room 30 m long, 24 m broad and 18 m high. (In my book the answer is 42.43 m)​

Answer 1

Answer:

Longest length of rod that can be placed = $30\sqrt{2} m$ = 42.4264m

Step-by-step explanation:

The room length = 30m

The room breadth = 24m

The room height = 18m

Using Pythagoras's theorem for right angled triangles:

Diagonal of the floor Squared = length squared + breadth squared

Now the longest diagonal of cuboid (room) squared

= Diagonal of the floor Squared + height squared

= (length squared + breadth squared) + height squared

= (30x30 + 24x24 + 18x18) square metres

=1800 square metres

=30x30x2 square metres

Therefor, longest length of rod that can be placed = $30\sqrt{2} m$ = 42.4264m