The length of longest rod that can be placed in a room 20 m long, 16 m broad and 12 m high, is----

Options

A. 20m
B. 16.4 m
C. 48m
D. 28.2m

Answer

To find the length of the longest rod that can be placed in a room with dimensions 20 m long, 16 m broad, and 12 m high, we need to calculate the diagonal of the cuboid formed by these dimensions.

### Step-by-Step Solution:

1. **Identify the dimensions of the room**:
- Length (L) = 20 m
- Breadth (B) = 16 m
- Height (H) = 12 m

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

3. **Substitute the values into the formula**:
\[ D = \sqrt{(20)^2 + (16)^2 + (12)^2} \]

4. **Calculate the squares of the dimensions**:
- \(20^2 = 400\)
- \(16^2 = 256\)
- \(12^2 = 144\)

5. **Add the squares**:
\[ D = \sqrt{400 + 256 + 144} \]
\[ D = \sqrt{800} \]

6. **Calculate the square root**:
\[ D = \sqrt{800} \approx 28.28 \text{ m} \]

7. **Final answer**:
The length of the longest rod that can be placed in the room is approximately **28.28 m**.