Find the length of the wire required to fence a square field 6 times having its area 5 hectares and 76 acres :

Options

A. 5760 m
B. 6760 m
C. 52500 m
D. 11760 m

Answer

To find the length of the wire required to fence a square field 6 times, given its area in hectares and acres, we can follow these steps:

### Step 1: Convert the Area to Square Meters
The area of the square field is given as 5 hectares and 76 acres. We need to convert this into square meters.

1 hectare = 10,000 square meters
1 acre = 4,046.86 square meters

Calculating the area:
- Area in hectares:
\( 5 \text{ hectares} = 5 \times 10,000 = 50,000 \text{ m}^2 \)

- Area in acres:
\( 76 \text{ acres} = 76 \times 4,046.86 \approx 307,000 \text{ m}^2 \)

- Total area:
\( 50,000 + 307,000 = 357,000 \text{ m}^2 \)

### Step 2: Calculate the Side Length of the Square
The area of a square is given by the formula:
\[ \text{Area} = \text{side}^2 \]

To find the side length, we take the square root of the area:
\[ \text{side} = \sqrt{357,000} \]

Calculating the square root:
\[ \text{side} \approx 597.5 \text{ m} \]

### Step 3: Calculate the Perimeter of the Square
The perimeter \( P \) of a square is given by:
\[ P = 4 \times \text{side} \]

Substituting the side length:
\[ P = 4 \times 597.5 \approx 2390 \text{ m} \]

### Step 4: Calculate the Total Length of Wire Required
Since we need to fence the square field 6 times, we multiply the perimeter by 6:
\[ \text{Total Length of Wire} = 6 \times P \]
\[ \text{Total Length of Wire} = 6 \times 2390 \approx 14340 \text{ m} \]

### Final Answer
The length of the wire required to fence the square field 6 times is approximately **14,340 meters**.

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