Two persons depart from their office towards their houses. First person goes 8 km in north direction and second person goes 6 km in east direction and reach their houses, find out the direct distance of their Houses?

Options

A. 10 km
B. 12 km
C. 14 km
D. 15 km

Answer

To find the direct distance between the two houses, we can use the Pythagorean theorem. The two persons have moved in perpendicular directions (one going north and the other going east), which forms a right triangle.

### Step-by-Step Solution:

1. **Identify the distances traveled by each person:**
- The first person travels 8 km north.
- The second person travels 6 km east.

2. **Visualize the scenario:**
- Imagine a right triangle where:
- One leg represents the distance traveled by the first person (8 km north).
- The other leg represents the distance traveled by the second person (6 km east).

3. **Apply the Pythagorean theorem:**
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
\[ c^2 = a^2 + b^2 \]
Here, \( a = 8 \) km and \( b = 6 \) km.

4. **Calculate the squares of the distances:**
\[ a^2 = 8^2 = 64 \]
\[ b^2 = 6^2 = 36 \]

5. **Sum the squares:**
\[ c^2 = 64 + 36 = 100 \]

6. **Find the hypotenuse (direct distance):**
\[ c = \sqrt{100} = 10 \text{ km} \]

### Conclusion:
The direct distance between the two houses is **10 km**.