What is the length (in metres) of the longest rod that can be placed in a room which is 2 metres long, 2 metres broad and 6 metres high?

Options

A. 8
B. `2sqrt(11)`
C. `3sqrt(11)`
D. 10

Answer

To find the length of the longest rod that can be placed in a room with dimensions 2 meters long, 2 meters broad, and 6 meters high, we need to calculate the diagonal of the cuboid formed by these dimensions.

### Step-by-Step Solution:

1. **Identify the dimensions of the cuboid**:
- Length (L) = 2 meters
- Breadth (B) = 2 meters
- Height (H) = 6 meters

2. **Use the formula for the diagonal of a cuboid**:
The formula to calculate the diagonal (D) of a cuboid is:
\[ D = \sqrt{L^2 + B^2 + H^2} \]

3. **Substitute the values into the formula**:
\[ D = \sqrt{(2)^2 + (2)^2 + (6)^2} \]

4. **Calculate the squares**:
- \( (2)^2 = 4 \)
- \( (2)^2 = 4 \)
- \( (6)^2 = 36 \)

5. **Add the squared values**:
\[ D = \sqrt{4 + 4 + 36} = \sqrt{44} \]

6. **Simplify the square root**:
\[ \sqrt{44} = \sqrt{4 \times 11} = \sqrt{4} \times \sqrt{11} = 2\sqrt{11} \]

7. **Final answer**:
The length of the longest rod that can be placed in the room is:
\[ 2\sqrt{11} \text{ meters} \]