Question

Find the length of the longest pole that can be put in a room having the dimensions 10m*10m*5m

Answer 1

The longest rod will be the diagonal of cuboidal room.
Length of diagonal : root (10^2+10^2+5^2) = root (225) = 15m

Answer 2

hi friend
here's your answer looking for

the length of longest pole in the cuboidal room will be the length of diagonal of that cuboidal room.

so,

the diagonals of the cuboid is
$\sqrt{ {l}^{2} + {b}^{2} + {h}^{2} }$
so,
the longest Pole =

$\sqrt{ {l}^{2} + {b}^{2} + {h}^{2} } \\ = \sqrt{ {10}^{2} + {10}^{2} + {5}^{2} } \\ = \sqrt{100 + 100 + 25} \\ = \sqrt{225} \\ = 15m$
so the length of longest pole in that cuboidal room will be equal to 15 m.

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hope you are satisfied with my answer