A park is 10 metres long and 8 metres broad. What is the length of the longest pole that can be placed in the park ?

Options

A. 10 metres
B. 12.8 metres
C. 13.4 metres
D. 18 metres

Answer

To find the length of the longest pole that can be placed in a park that is 10 meters long and 8 meters broad, we can use the Pythagorean theorem. The longest pole will be placed diagonally across the park.

### Step-by-Step Solution:

1. **Identify the dimensions of the park:**
- Length (AB) = 10 meters
- Breadth (BC) = 8 meters

2. **Visualize the park as a rectangle:**
- The corners of the rectangle can be labeled as A (0,0), B (10,0), C (10,8), and D (0,8).
- The diagonal we want to find is AC.

3. **Apply the Pythagorean theorem:**
- The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC).
- Mathematically, this can be expressed as:
\[ AC^2 = AB^2 + BC^2 \]

4. **Substitute the values into the equation:**
- \( AC^2 = 10^2 + 8^2 \)
- \( AC^2 = 100 + 64 \)
- \( AC^2 = 164 \)

5. **Calculate the length of AC:**
- To find AC, take the square root of 164:
\[ AC = \sqrt{164} \]

6. **Estimate the square root:**
- We know that \( 12^2 = 144 \) and \( 13^2 = 169 \).
- Since \( 164 \) is between \( 144 \) and \( 169 \), we can conclude that \( \sqrt{164} \) is between \( 12 \) and \( 13 \).
- A more precise approximation shows that \( \sqrt{164} \) is approximately \( 12.81 \).

7. **Conclusion:**
- The length of the longest pole that can be placed in the park is approximately \( 12.81 \) meters.