Two poles of the height 15 m and 20 m stand vertically upright on a plane ground. If the distance between their feet is 12 m, find distance betwene their tops.
A. 11 m
B. 12 m
C. 13 m
D. 14 m

Options

A. A
B. D
C. B
D. C

Answer

To solve the problem of finding the distance between the tops of two poles of heights 15 m and 20 m that stand 12 m apart, we can follow these steps:

### Step 1: Understand the Geometry
We have two vertical poles:
- Pole A (height = 20 m)
- Pole B (height = 15 m)

The distance between the feet of the poles (the horizontal distance) is given as 12 m.

### Step 2: Determine the Height Difference
The difference in height between the two poles can be calculated as:
\[ \text{Height difference} = \text{Height of Pole A} - \text{Height of Pole B} \]
\[ \text{Height difference} = 20 \, \text{m} - 15 \, \text{m} = 5 \, \text{m} \]

### Step 3: Create a Right Triangle
We can visualize the situation as a right triangle where:
- One leg (vertical) represents the height difference (5 m).
- The other leg (horizontal) represents the distance between the feet of the poles (12 m).
- The hypotenuse represents the distance between the tops of the poles.

### Step 4: Apply the Pythagorean Theorem
Using the Pythagorean theorem, we can find the length of the hypotenuse (distance between the tops of the poles):
\[ c^2 = a^2 + b^2 \]
Where:
- \( c \) is the hypotenuse (distance between the tops of the poles).
- \( a \) is the height difference (5 m).
- \( b \) is the distance between the feet of the poles (12 m).

Substituting the values:
\[ c^2 = (5 \, \text{m})^2 + (12 \, \text{m})^2 \]
\[ c^2 = 25 + 144 \]
\[ c^2 = 169 \]

### Step 5: Calculate the Hypotenuse
Now, take the square root to find \( c \):
\[ c = \sqrt{169} = 13 \, \text{m} \]

### Conclusion
The distance between the tops of the two poles is **13 m**.

### Answer
C. 13 m

---