The length of the longest rod which can be laid across a floor of a rectangular room 12 m in length and 5 m in breadth will be:

Options

A. 17m
B. 7m
C. 12m
D. 13m

Answer

To find the length of the longest rod that can be laid across a rectangular room, we need to calculate the diagonal of the rectangle. The formula for the diagonal \(d\) of a rectangle with length \(l\) and breadth \(b\) is given by the Pythagorean theorem:

\[ d = \sqrt{l^2 + b^2} \]

### Step-by-Step Solution:

1. **Identify the dimensions of the rectangle**:
- Length \(l = 12 \, \text{m}\)
- Breadth \(b = 5 \, \text{m}\)

2. **Apply the Pythagorean theorem**:
- Substitute the values into the formula:
\[ d = \sqrt{12^2 + 5^2} \]

3. **Calculate the squares**:
- Calculate \(12^2\):
\[ 12^2 = 144 \]
- Calculate \(5^2\):
\[ 5^2 = 25 \]

4. **Add the squares**:
- Now add the results:
\[ 144 + 25 = 169 \]

5. **Take the square root**:
- Finally, take the square root of the sum:
\[ d = \sqrt{169} = 13 \, \text{m} \]

### Conclusion:
The length of the longest rod that can be laid across the floor of the rectangular room is **13 meters**.