A man goes to a garden and runs in the following manner: From the starting point, he goes west 25 m, then due north 60 m, then due east 80 m and finally due south 12 m. The distance between the finishing point and the starting point is :

Options

A. 177 m
B. 103 m
C. 83 m
D. 73 m

Answer

To find the distance between the finishing point and the starting point of the man's run in the garden, we can follow these steps:

### Step 1: Determine the coordinates of each point
- **Starting Point (S)**: Let's assume the starting point is at the origin (0, 0).
- **After going West 25 m**: The new position will be (0 - 25, 0) = (-25, 0).
- **After going North 60 m**: The new position will be (-25, 0 + 60) = (-25, 60).
- **After going East 80 m**: The new position will be (-25 + 80, 60) = (55, 60).
- **After going South 12 m**: The new position will be (55, 60 - 12) = (55, 48).

### Step 2: Calculate the distance between the starting point and the finishing point
The starting point S is at (0, 0) and the finishing point F is at (55, 48). We can use the distance formula to find the distance \( d \) between these two points:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substituting the coordinates:
\[ d = \sqrt{(55 - 0)^2 + (48 - 0)^2} \]
\[ d = \sqrt{55^2 + 48^2} \]

### Step 3: Calculate \( 55^2 \) and \( 48^2 \)
\[ 55^2 = 3025 \]
\[ 48^2 = 2304 \]

### Step 4: Add the squares
\[ d = \sqrt{3025 + 2304} \]
\[ d = \sqrt{5329} \]

### Step 5: Calculate the square root
\[ d = 73 \text{ m} \]

### Final Answer
The distance between the finishing point and the starting point is **73 meters**.

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