If person travels from a point L towards east for 12km and then 5 km towards north and reaches a point M, then shortest distance from L to M is :

Options

A. 17 km
B. 13 km
C. 14 km
D. 12 km

Answer

To find the shortest distance from point L to point M, we can use the Pythagorean theorem. Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Understand the Movement**:
- The person travels from point L towards the east for 12 km.
- Then, the person travels north for 5 km to reach point M.

2. **Visualize the Path**:
- The path forms a right triangle where:
- The eastward movement (12 km) is one leg of the triangle (base).
- The northward movement (5 km) is the other leg of the triangle (perpendicular).

3. **Identify the Triangle**:
- Let:
- \( a = 12 \) km (base)
- \( b = 5 \) km (perpendicular)
- \( c \) = distance from L to M (hypotenuse)

4. **Apply the Pythagorean Theorem**:
- According to the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
- Substitute the values:
\[ c^2 = 12^2 + 5^2 \]
- Calculate the squares:
\[ c^2 = 144 + 25 \]
- Add the results:
\[ c^2 = 169 \]

5. **Calculate the Hypotenuse**:
- To find \( c \), take the square root of 169:
\[ c = \sqrt{169} = 13 \text{ km} \]

6. **Conclusion**:
- The shortest distance from point L to point M is **13 km**.