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Question

Mathematics Question on Geometry

The length of the longest rod that can be placed in a room which is 12 m long 9 m broad and 8 m high is

A

27 m

B

19m

C

17 m

D

13 m

Answer

17 m

Explanation

Solution

The correct option is (C): 17 m
Explanation: To find the length of the longest rod that can be placed in the room, we need to calculate the length of the diagonal of the rectangular room. The formula for the diagonal dd of a cuboid (rectangular prism) is given by:
d=l2+b2+h2d = \sqrt{l^2 + b^2 + h^2}
where ll is the length, bb is the breadth, and hh is the height.
Given:
- Length l=12l = 12 m
- Breadth b=9b = 9 m
- Height h=8h = 8 m
Substituting the values:
d=122+92+82=144+81+64=289=17 md = \sqrt{12^2 + 9^2 + 8^2} = \sqrt{144 + 81 + 64} = \sqrt{289} = 17 \text{ m}
Therefore, the length of the longest rod that can be placed in the room is 17 m.