Question

The length of the longest pole that can be placed in a room 12 m long, 9 m wide and 8 m high, is

Answer 1

Given length l = 12 m
breadth b = 9 m and height h = 8 m
Longest rod that can be placed in a room is nothing but its diagonal.
Length of diagonal of a cuboid = √(l2 + b2 + h2)
Length of longest rod = √(122 + 92 + 82) m
= √(144 + 81 + 64) m
= √289 m
= 17 m
Thus the length of the longest rod is 17 m

Answer 2

it's the diagonal length of the room given by

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

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

$d = \sqrt{144 + 81 + 64} = \sqrt{289} = 17$

therefore the longest pole that can be kept in the room is 17 m