# Find the length of the longest iron rod that can be placed in a room 30 m long 24 m broad and 12 root 2 high

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dimensions of room length 30 m , breadth 24 m and height 12 m height .

The diagonal of the base =

= 38.418 m

Longest diagonal =

= 42 m

Therefore the longest iron rod that can be placed = 42 m

dimensions are length =30m

breadth = 24 m

height = 12√2 m

in the diagram green line = 38.4 m

( by pythagoras theorem , green line = √(24² + 30²)

=√(576 + 900)

= √1476

= 38.4 m )

now, red line = (12√2)² + (38.4)²

=√( 288 + 1474.56)

= √1762.56

= 41.98 m

therefore, the length of longest iron rod that can be placed in the room = 42 m (nearly 41.98 m)