What is the perimeter of the semi-circular field, whose area is 15400 sq. m?

Options

A. `460sqrt2m`
B. `360sqrt2m`
C. `260sqrt2m`
D. `160sqrt2m`

Answer

To find the perimeter of the semi-circular field whose area is 15400 sq. m, we can follow these steps:

### Step 1: Understand the formula for the area of a semicircle
The area \( A \) of a semicircle is given by the formula:
\[ A = \frac{1}{2} \pi r^2 \]
where \( r \) is the radius of the semicircle.

### Step 2: Set up the equation using the given area
We know the area of the semicircle is 15400 sq. m. Thus, we can set up the equation:
\[ \frac{1}{2} \pi r^2 = 15400 \]

### Step 3: Solve for \( r^2 \)
To isolate \( r^2 \), we first multiply both sides by 2:
\[ \pi r^2 = 30800 \]
Next, we divide both sides by \( \pi \):
\[ r^2 = \frac{30800}{\pi} \]

### Step 4: Substitute the value of \( \pi \)
Using \( \pi \approx \frac{22}{7} \), we can substitute:
\[ r^2 = \frac{30800 \times 7}{22} \]
Calculating this gives:
\[ r^2 = \frac{215600}{22} = 9800 \]

### Step 5: Calculate \( r \)
Now, we take the square root of both sides to find \( r \):
\[ r = \sqrt{9800} = 70 \text{ m} \]

### Step 6: Find the perimeter of the semicircle
The perimeter \( P \) of a semicircle is given by:
\[ P = \pi r + 2r \]
Substituting the value of \( r \):
\[ P = \pi \times 70 + 2 \times 70 \]
Using \( \pi \approx \frac{22}{7} \):
\[ P = \frac{22}{7} \times 70 + 140 \]
Calculating \( \frac{22}{7} \times 70 \):
\[ P = 220 + 140 = 360 \text{ m} \]

### Final Answer
Thus, the perimeter of the semicircular field is:
\[ \boxed{360 \text{ m}} \]