Distance covered by a man 3 times around a square park having side 3x -2a + 5 is

Options

A. 9x -6a +15
B. 12 x - 4a + 20
C. 36x - 24a + 60
D. None of these

Answer

To find the distance covered by a man who walks 3 times around a square park with a side length of \(3x - 2a + 5\), we can follow these steps:

### Step 1: Identify the side length of the square park
The side length of the square park is given as:
\[ \text{Side} = 3x - 2a + 5 \]

### Step 2: Calculate the perimeter of the square park
The perimeter \(P\) of a square is calculated using the formula:
\[ P = 4 \times \text{Side} \]
Substituting the side length:
\[ P = 4 \times (3x - 2a + 5) \]

### Step 3: Simplify the perimeter
Now, we simplify the expression:
\[ P = 4(3x) - 4(2a) + 4(5) \]
\[ P = 12x - 8a + 20 \]

### Step 4: Calculate the total distance covered by walking 3 times around the park
To find the total distance \(D\) covered by walking around the park 3 times, we multiply the perimeter by 3:
\[ D = 3 \times P \]
Substituting the perimeter we calculated:
\[ D = 3 \times (12x - 8a + 20) \]

### Step 5: Simplify the total distance
Now, we simplify this expression:
\[ D = 3 \times 12x - 3 \times 8a + 3 \times 20 \]
\[ D = 36x - 24a + 60 \]

### Final Answer
The total distance covered by the man is:
\[ D = 36x - 24a + 60 \]

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