Question

Find the length of the longest rod that can be placed in a room of dimension 10m x 8mx6m.

Answer 1

Answer:

the diagonal of the cuboid

Step-by-step exit is planation:

D =√l²+b²+h³

D=√10²+8²+6²

D=√100+64+36

D=√200

D=10√2

∴ THE LENGTH OF THE LONGEST ROD THAT CAN BE PLACED= 10√2 m

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Answer 2

Here,

From the dimensions given, we can conclude that the shape of room is of $\sf{\underline{Cuboid}}$ shape.

Dimensions of the room –

Length, l = 10 m

Breadth, b = 8 m

Height, h = 6 m

Now,

The rod should be placed $\sf{\underline{diagonally}}$.

Diagonal of the Cuboid -

= $\sf{{\sqrt{l^2 + b^2 + h^2}}}$

= $\sf{{\sqrt{10^2 + 8^2 + 6^2}}}$

= $\sf{{\sqrt{100 + 64 + 36}}}$

= $\sf{{\sqrt{200}}}$

= $\sf{10 {\sqrt{2}}}$

Hence, length of the longest rod =
${\boxed{\sf{10 {\sqrt{2}} \ m}}}$.