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 ?

Question

Accepted Answer

To determine the direct distance between the two houses, we can use the Pythagorean theorem. The scenario described forms a right-angled triangle where the first person travels 8 km north and the second person travels 6 km east. These distances represent the two perpendicular sides of the triangle.

1. **Explanation for Option 1 (10 Km):**

According to the Pythagorean theorem, the direct distance (hypotenuse) between the two houses can be calculated using the formula:
   
   $$
   c = \sqrt{a^2 + b^2}
   $$

where $ a $ and $ b $ are the lengths of the two perpendicular sides of the triangle.

Here, $ a = 8 $ km and $ b = 6 $ km. Plugging these values into the formula gives:

$$
   c = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \text{ km}
   $$

Therefore, the direct distance between their houses is 10 km, which corresponds to Option 1.

2. **Explanation for why other options are incorrect:**

- **Option 2 (12 Km):** If the direct distance were 12 km, the calculation would be incorrect as it does not satisfy the Pythagorean theorem with the given side lengths of 8 km and 6 km. The calculation would result in a hypotenuse of 10 km, not 12 km.

- **Option 3 (14 Km):** Similarly, a direct distance of 14 km would not satisfy the Pythagorean theorem for the given side lengths. The calculated hypotenuse is 10 km, not 14 km.

- **Option 4 (15 Km):** A direct distance of 15 km is also incorrect as it does not match the result from the Pythagorean theorem. The correct hypotenuse is 10 km, not 15 km.

In conclusion, the correct direct distance between the two houses is 10 km, which is why Option 1 is the correct answer.