Question:
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
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
Updated On: Sep 25, 2024
- 27 m
- 19m
- 17 m
- 13 m
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The Correct Option is C
Solution and Explanation
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 \(d\) of a cuboid (rectangular prism) is given by:
\[d = \sqrt{l^2 + b^2 + h^2}\]
where \(l\) is the length, \(b\) is the breadth, and \(h\) is the height.
Given:
- Length \(l = 12\) m
- Breadth \(b = 9\) m
- Height \(h = 8\) m
Substituting the values:
\[d = \sqrt{12^2 + 9^2 + 8^2} = \sqrt{144 + 81 + 64} = \sqrt{289} = 17 \text{ m}\]
Therefore, the length of the longest rod that can be placed in the room is 17 m.
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 \(d\) of a cuboid (rectangular prism) is given by:
\[d = \sqrt{l^2 + b^2 + h^2}\]
where \(l\) is the length, \(b\) is the breadth, and \(h\) is the height.
Given:
- Length \(l = 12\) m
- Breadth \(b = 9\) m
- Height \(h = 8\) m
Substituting the values:
\[d = \sqrt{12^2 + 9^2 + 8^2} = \sqrt{144 + 81 + 64} = \sqrt{289} = 17 \text{ m}\]
Therefore, the length of the longest rod that can be placed in the room is 17 m.
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