Two poles of height 7 metres and 12 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 find 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 use the Pythagorean theorem. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We have two poles:
- Pole A (height = 12 meters)
- Pole B (height = 7 meters)

The distance between the feet of the poles (the horizontal distance) is 12 meters.

### Step 2: Determine the Height Difference
Calculate the vertical distance between the tops of the poles:
- Height of Pole A = 12 meters
- Height of Pole B = 7 meters

The height difference (vertical distance) between the tops of the poles is:
\[ \text{Height Difference} = \text{Height of Pole A} - \text{Height of Pole B} = 12 - 7 = 5 \text{ meters} \]

### Step 3: Set Up the Right Triangle
We can visualize this situation as a right triangle where:
- One leg (vertical leg) is the height difference (5 meters).
- The other leg (horizontal leg) is the distance between the feet of the poles (12 meters).

### Step 4: Apply the Pythagorean Theorem
According to the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
where:
- \( c \) is the distance between the tops of the poles,
- \( a \) is the height difference (5 meters),
- \( b \) is the distance between the feet of the poles (12 meters).

Substituting the values:
\[ c^2 = 5^2 + 12^2 \]
\[ c^2 = 25 + 144 \]
\[ c^2 = 169 \]

### Step 5: Calculate the Distance
Now, take the square root of both sides to find \( c \):
\[ c = \sqrt{169} = 13 \text{ meters} \]

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

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