Two poles of height 7 metre and 12 metre stand on a plane ground. If the distance between their feet is 12 metre, the distance between their top will be

Options

A. 15 metre
B. 13 metre
C. 19 metre
D. 17 metre

Answer

To solve the problem of finding the distance between the tops of two poles of heights 7 meters and 12 meters, which are 12 meters apart at their bases, we can follow these steps:

### Step-by-Step Solution:

1. **Draw a Diagram**:
- Visualize the two poles standing vertically on the ground. Label the top of the 7-meter pole as point A and the top of the 12-meter pole as point B. The feet of the poles are points C and D respectively, with the distance between C and D being 12 meters.

2. **Identify the Heights**:
- The height of pole A (7 meters) is represented as AC = 7 meters.
- The height of pole B (12 meters) is represented as BD = 12 meters.

3. **Determine the Vertical Distance Between the Tops of the Poles**:
- The vertical distance between the tops of the poles (AB) can be calculated as the difference in their heights:
\[ \text{Vertical Distance} = BD - AC = 12 \text{ m} - 7 \text{ m} = 5 \text{ m} \]

4. **Form a Right Triangle**:
- We can form a right triangle with:
- AC as one leg (5 meters, the difference in height),
- CD as the other leg (12 meters, the distance between the feet of the poles),
- AB as the hypotenuse (the distance between the tops of the poles).

5. **Apply the Pythagorean Theorem**:
- According to the Pythagorean theorem:
\[ AB^2 = AC^2 + CD^2 \]
- Substitute the values:
\[ AB^2 = (5 \text{ m})^2 + (12 \text{ m})^2 \]
\[ AB^2 = 25 + 144 = 169 \]

6. **Calculate the Length of AB**:
- To find AB, take the square root of 169:
\[ AB = \sqrt{169} = 13 \text{ m} \]

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