The length, breadth and height of a room is 21 metres, 12 metres and 16 metres. What will be the length of the largest rod that can be placed in that room?

Options

A. 32 metres
B. 25 metres
C. 31 metres
D. 29 metres

Answer

To find the length of the largest rod that can be placed in a room with given dimensions, we need to calculate the diagonal of the cuboidal room. The formula for the diagonal \(d\) of a cuboid is given by:

\[ d = \sqrt{L^2 + B^2 + H^2} \]

where:
- \(L\) is the length of the room,
- \(B\) is the breadth of the room,
- \(H\) is the height of the room.

### Step-by-step Solution:

1. **Identify the dimensions of the room**:
- Length \(L = 21\) metres
- Breadth \(B = 12\) metres
- Height \(H = 16\) metres

2. **Substitute the dimensions into the diagonal formula**:
\[ d = \sqrt{21^2 + 12^2 + 16^2} \]

3. **Calculate the squares of the dimensions**:
- \(21^2 = 441\)
- \(12^2 = 144\)
- \(16^2 = 256\)

4. **Add the squares together**:
\[ 441 + 144 + 256 = 841 \]

5. **Take the square root of the sum**:
\[ d = \sqrt{841} = 29 \]

6. **Conclusion**:
The length of the largest rod that can be placed in the room is \(29\) metres.

### Final Answer:
The correct answer is \(29\) metres.

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