Two poles of heights 8m and 13 m stands on a plane ground. If the distance between the feet of the poles is `12m`, find the distance between their tops.

Answer

To solve the problem of finding the distance between the tops of two poles of heights 8 m and 13 m that are 12 m apart, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the heights of the poles**:
- Let the height of the first pole (Pole A) be 8 m.
- Let the height of the second pole (Pole B) be 13 m.

2. **Determine the vertical distance between the tops of the poles**:
- The vertical distance between the tops of the two poles can be found by subtracting the height of the shorter pole from the height of the taller pole.
- Vertical distance = Height of Pole B - Height of Pole A = 13 m - 8 m = 5 m.

3. **Draw a right triangle**:
- The distance between the feet of the poles is the base of the triangle, which is 12 m.
- The vertical distance we calculated is the height of the triangle, which is 5 m.

4. **Apply the Pythagorean theorem**:
- According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (L) is equal to the sum of the squares of the other two sides (height and base).
- Thus, we have:
\[ L^2 = (Base)^2 + (Height)^2 \]
\[ L^2 = (12 m)^2 + (5 m)^2 \]
\[ L^2 = 144 + 25 \]
\[ L^2 = 169 \]

5. **Calculate the length of the hypotenuse**:
- To find L, take the square root of both sides:
\[ L = \sqrt{169} = 13 m \]

6. **Conclusion**:
- The distance between the tops of the two poles is 13 m.

### Final Answer:
The distance between the tops of the two poles is **13 meters**.