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 out how far the boy is from the starting point after walking 12 m due east and then 5 m due south, we can use the Pythagorean theorem. Here’s the step-by-step solution:

### Step 1: Understand the movement
The boy walks:
- 12 m due east (let's call this distance AB)
- 5 m due south (let's call this distance BC)

### Step 2: Visualize the path
We can visualize the boy's path as a right triangle:
- Point A is the starting point.
- Point B is where he ends up after walking east.
- Point C is where he ends up after walking south.

### Step 3: Identify the sides of the triangle
In this right triangle:
- AB = 12 m (the horizontal leg)
- BC = 5 m (the vertical leg)
- AC is the hypotenuse, which represents the distance from the starting point A to the final point C.

### Step 4: Apply the Pythagorean theorem
According to the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]
Substituting the known values:
\[ AC^2 = 12^2 + 5^2 \]

### Step 5: Calculate the squares
Calculating the squares:
\[ 12^2 = 144 \]
\[ 5^2 = 25 \]

### Step 6: Add the squares
Now, add these values:
\[ AC^2 = 144 + 25 = 169 \]

### Step 7: Find the square root
To find AC, we take the square root of both sides:
\[ AC = \sqrt{169} = 13 \]

### Conclusion
The distance from the starting point to the final point is **13 meters**.

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