# Find the length of the longest rod that can be placed in a room 16m long 12m broad and 32/3 m high.

Here l=16m, b=12m, h=$\frac{32}{3}m$
The length of the longest pole = Length of the diagonal
$\sqrt {l^{2}+b^{2}+h^{2}}=\sqrt{(16)^{2}+(12)^{2}+(\frac{32}{3})^{2}}\, m$
$=\sqrt{256+144+\frac{1024}{9}}\, m$
$=\sqrt{\frac{4624}{9}}\, m$
$=\frac{68}{3}\, m$
$\Rightarrow 22\tfrac{2}{3}m$

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