The length of the longest pole that can be put in a room (25 metress `xx 12` metres `xx8` metres) is-

Options

A. 25 metres
B. 45 metres
C. `27cdot7` metres
D. `28cdot8` metres

Answer

To find the length of the longest pole that can be placed in a room with dimensions 25 meters, 12 meters, and 8 meters, we need to calculate the diagonal of the room. The formula for the diagonal \(d\) of a rectangular prism (room) 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 \(L = 25\) meters
- Breadth \(B = 12\) meters
- Height \(H = 8\) meters

2. **Substitute the values into the formula**:
\[ d = \sqrt{(25)^2 + (12)^2 + (8)^2} \]

3. **Calculate the squares of each dimension**:
- \(L^2 = 25^2 = 625\)
- \(B^2 = 12^2 = 144\)
- \(H^2 = 8^2 = 64\)

4. **Add the squares together**:
\[ 625 + 144 + 64 = 833 \]

5. **Take the square root of the sum**:
\[ d = \sqrt{833} \]

6. **Calculate the square root**:
\[ d \approx 28.8 \text{ meters} \]

Thus, the length of the longest pole that can be placed in the room is approximately **28.8 meters**.