Question

What is the length on the longest rod that can be placed in a room of 5 m *4m*3 m
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Answer 1

$\huge\text{\underline{Answer}}$

$\sf{\underline{Given }}$

A room having dimension = 5m × 4m × 3m

Find the length of longest rod = ?

$\huge\sf{solution:}$

Since, the dimension of cuboid is given,

Length of longest rod is given by length of diagonal of cuboid.

Diagonal of cuboid = $\boxed{\sf{\sqrt{ {l}^{2} + {b}^{2} + {h}^{2} } }}$

Now,put the dimension is formula.

Diagonal of cuboid =

$\implies$ $\bold{ \sqrt{ {5}^{2} + {4}^{2} + {3}^{2} } }$

$\implies$ $\bold{ \sqrt{25 + 16 + 9} }$

$\implies$ $\bold{ \sqrt{50} }$

Length of longest rod $\implies$ $\bold{ 5 \sqrt{2} m}$

hence, the length of longest rod kept in cuboidal room is $\bold{5 \sqrt{2} }$m