Question

find the length of the longest rod that can be placed in a room of dimension 10m × 8m×6m

Answer 1

Here is your solutions

Given :-

a room of dimension 10m × 8m×6m (dimensions in shape of cuboid )

To find length of the longest rod.

Diagonal of cuboid = longest rode

so we will find Diagonal of cuboid

$d = \sqrt{l {}^{2} + h {}^{2} + b {}^{2} } \\ d = \sqrt{10 {}^{2} + 8 {}^{2} + 6 {}^{2} } \\ d = \sqrt{100 + 64 + 36} \\ d = \sqrt{200} \\ d = 10 \sqrt{2} \: m$
Hope it helps you

Answer 2

Solutions :-

Given :
Dimension of room = 10 m × 8 m × 6 m

So,
Length = l = 10 m
Breadth = b = 8 m
Height = h = 6 m

Find the length of the longest rod :-

$\bold {Diagonal~ of ~cuboid~ =~ \sqrt{l^2 + b^2 + h^2}~unit }$

$= \sqrt{ {10}^{2} + {8}^{2} + {6}^{2} } \: \: m\\ \\ = \sqrt{100 + 64 + 36} \: \: m \\ \\ = \sqrt{200} \: \: m \\ \\ = \sqrt{2 \times 2 \times 2 \times 5 \times 5} \: \: m \\ \\ = 2 \times 5 \times \sqrt{2} \: \: m\\ \\ = 10 \sqrt{2} \: \: m$

Hence,
The length of the longest rod = 10√2 m