Question

find the length of longest rod that can be placed in a room 16m long, 12m broad and 10 2/3 m high

Answer 1

Answer:

Since the room is in cuboid shape

Length of largest rod = Diagonal of

cuboid

=12+b2+h2--------------√

=162+122+32232---------------√

=256+144+10249-----------------√

=2304+1296+10249----------------√

=46249-----------√=683

=2223m

Answer 2

Given :-

• Length of room = 16m
• Breadth of room = 12m
• Height of room = 10 ⅔m

To find :-

• Length of the Longest rod

✯Longest rod is the diagonal✯

✯Here, the room is cuboidal in shape✯

Solution :-

• Length of Diagonal (Cuboid) = √l² + b² + h²

• Length of Diagonal (Cuboid) = √16² + 12² + ³²⁄₃²

• Length of Diagonal (Cuboid) = √256 + 144 + ¹⁰²⁴⁄₉

• Length of Diagonal (Cuboid) = √⁴⁶²⁴⁄₉

• Length of Diagonal (Cuboid) = ⁶⁸⁄₉ = 22 ⅔

∴ The length of the longest rod or diagonal = 22 ⅔m