A boy walks 12 m due east and 5 m due south. How far is he from the starting point?

Options

A. 12 M
B. 17 M
C. 13 M
D. 20 M

Answer

To find the distance of the boy from the starting point after walking 12 meters due east and 5 meters due south, we can use the Pythagorean theorem. Here are the steps:

### Step-by-Step Solution:

1. **Understanding the Movement**:
- The boy walks 12 meters east and 5 meters south. We can visualize this as forming a right triangle where:
- One leg of the triangle (eastward movement) is 12 meters.
- The other leg of the triangle (southward movement) is 5 meters.

2. **Identifying the Right Triangle**:
- The distance from the starting point to the final position is the hypotenuse of the right triangle formed by the two legs (12 meters and 5 meters).

3. **Applying 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, let \( a = 12 \) meters and \( b = 5 \) meters.
- Therefore:
\[ c^2 = 12^2 + 5^2 \]

4. **Calculating the Squares**:
- Calculate \( 12^2 \):
\[ 12^2 = 144 \]
- Calculate \( 5^2 \):
\[ 5^2 = 25 \]

5. **Adding the Squares**:
- Now, add the two results:
\[ c^2 = 144 + 25 = 169 \]

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

7. **Conclusion**:
- The distance of the boy from the starting point is 13 meters.

### Final Answer:
The boy is 13 meters away from the starting point.