Question

Find the length of the longest rod that can be placed in a room 12m. Long, 9m board and 8m high?

Answer 1

Answer:

17m

Step-by-step explanation:

Given:- length, breadth, height of cuboid

To find:- Max length of road

Proof:-

The max length that can be inscribed in a cuboid is √(length2+ breadth2+ height2)

=√(144+81+64)=√289 = 17m

Hence Result

Hope this helps!

Answer 2

Answer:

If the length=a unit =12m, breadth=b unit =9m, and height=c unit= 8m of the room,

then the longest rod that can be placed in room=the length of the diagonal of a room.

$length \: of \: a \: diagonal \: of \: a \: cuboid \: = \sqrt{ {a}^{2} + {b}^{2} + {c}^{2} } unit$

$= \sqrt{ {12}^{2} + {9}^{2} + {8}^{2} } {m}^{2}$

$= \sqrt{144 + 81 + 64} {m}^{2}$

$= \sqrt{289} {m}^{2}$

$= 17m$

The longest rod that can be placed in a room is 17m