The length, breadth and height of room is 16 metres, 12 metres and 15 metres. What will be the length of the largest rod that can be placed in that room?

Options

A. 2 metres
B. 18 metres
C. 25 metres
D. 24 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 cuboid formed by the room. The dimensions of the room are:

- Length (L) = 16 meters
- Breadth (B) = 12 meters
- Height (H) = 15 meters

### Step-by-Step Solution:

1. **Identify the Formula for the Diagonal of a Cuboid**:
The formula to calculate the diagonal (D) of a cuboid is given by:
\[ D = \sqrt{L^2 + B^2 + H^2} \]

2. **Substitute the Values into the Formula**:
Now, substitute the values of L, B, and H into the formula:
\[ D = \sqrt{16^2 + 12^2 + 15^2} \]

3. **Calculate the Squares**:
Calculate the squares of each dimension:
- \( 16^2 = 256 \)
- \( 12^2 = 144 \)
- \( 15^2 = 225 \)

4. **Add the Squares Together**:
Now, add these squared values together:
\[ 256 + 144 + 225 = 625 \]

5. **Take the Square Root**:
Finally, take the square root of the sum to find the diagonal:
\[ D = \sqrt{625} = 25 \]

Thus, the length of the largest rod that can be placed in the room is **25 meters**.