The length of the longest rod that can be placed in a room of dimensions `(10 m xx 10 m xx 5m)` is

Options

A. 15m
B. 16m
C. `10 sqrt5 m`
D. 12 m

Explanation

To find the length of the longest rod that can be placed in a room with dimensions \(10 \, \text{m} \times 10 \, \text{m} \times 5 \, \text{m}\), we need to calculate the diagonal of the cuboid formed by these dimensions. The formula for the diagonal \(d\) of a cuboid is given by:

\[ d = \sqrt{L^2 + B^2 + H^2} \]

where \(L\) is the length, \(B\) is the breadth, and \(H\) is the height of the cuboid.

### Step-by-Step Solution:

1. **Identify the dimensions of the room:**
- Length \(L = 10 \, \text{m}\)
- Breadth \(B = 10 \, \text{m}\)
- Height \(H = 5 \, \text{m}\)

2. **Substitute the dimensions into the diagonal formula:**
\[ d = \sqrt{L^2 + B^2 + H^2} = \sqrt{10^2 + 10^2 + 5^2} \]

3. **Calculate each term inside the square root:**
- \(L^2 = 10^2 = 100\)
- \(B^2 = 10^2 = 100\)
- \(H^2 = 5^2 = 25\)

4. **Add the squared values:**
\[ L^2 + B^2 + H^2 = 100 + 100 + 25 = 225 \]

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

### Final Answer:
The length of the longest rod that can be placed in the room is **15 meters**.

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