Find the length of the largest pole that can be placed in a hall 10 m long, 10 m wide and 5 m high.[Hint. Length of the diagonal of the room =`sqrt(l^(2) +b^(2)+h^(2))`].

Answer

To find the length of the largest pole that can be placed in a hall with dimensions 10 m long, 10 m wide, and 5 m high, we will calculate the diagonal of the hall using the formula provided.

### Step-by-Step Solution:

1. **Identify the dimensions of the hall:**
- Length (l) = 10 m
- Width (b) = 10 m
- Height (h) = 5 m

2. **Use the formula for the diagonal of a rectangular prism:**
\[ \text{Diagonal} = \sqrt{l^2 + b^2 + h^2} \]

3. **Substitute the values into the formula:**
\[ \text{Diagonal} = \sqrt{(10)^2 + (10)^2 + (5)^2} \]

4. **Calculate the squares:**
- \(10^2 = 100\)
- \(10^2 = 100\)
- \(5^2 = 25\)

5. **Add the squared values:**
\[ 100 + 100 + 25 = 225 \]

6. **Take the square root of the sum:**
\[ \text{Diagonal} = \sqrt{225} = 15 \text{ m} \]

7. **Conclusion:**
The length of the largest pole that can be placed in the hall is **15 meters**.