Two poles of height 7 m and 12 m stand on a playground. If the distance between their feet is 12 m, then the distance between their tops is

Options

A. 12 m
B. 11 m
C. 13 m
D. 15 m

Answer

To find the distance between the tops of the two poles, we can visualize the situation as a right triangle. The two poles represent the vertical sides of the triangle, and the distance between their feet represents the horizontal side.

### Step-by-Step Solution:

1. **Identify the heights of the poles**:
- Height of the first pole (Pole A) = 7 m
- Height of the second pole (Pole B) = 12 m

2. **Calculate the difference in height**:
- Difference in height = Height of Pole B - Height of Pole A
- Difference in height = 12 m - 7 m = 5 m

3. **Identify the distance between the feet of the poles**:
- Distance between the feet = 12 m

4. **Use the Pythagorean theorem to find the distance between the tops of the poles**:
- Let \( d \) be the distance between the tops of the poles.
- According to the Pythagorean theorem:
\[ d^2 = (\text{Difference in height})^2 + (\text{Distance between feet})^2 \]
- Substitute the values:
\[ d^2 = (5 m)^2 + (12 m)^2 \]
\[ d^2 = 25 + 144 \]
\[ d^2 = 169 \]
- Taking the square root of both sides:
\[ d = \sqrt{169} = 13 m \]

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