Question

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

Answer 1

dimensions of room length 30 m , breadth 24 m and height 12$\sqrt{2}$ m height .
The diagonal of the base =  $\sqrt{30 ^{2}+24^{2} }$
                                            = 38.418 m
Longest diagonal = $\sqrt{38.418 ^{2}+(12\sqrt{2})^{2} }$
                              = 42 m
Therefore the longest iron rod that can be placed = 42 m

Answer 2

given,
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)