To solve this problem, let's follow these steps:
### Step 1: Determine the Side Length of the Square
The area of a square is found using the formula:
[tex]\[ \text{Area} = \text{Side length}^2 \][/tex]
Given that the area of the square plot is 2116 square meters:
[tex]\[ \text{Side length}^2 = 2116 \][/tex]
Taking the square root of both sides to find the side length:
[tex]\[ \text{Side length} = \sqrt{2116} \][/tex]
[tex]\[ \text{Side length} = 46 \, \text{meters} \][/tex]
### Step 2: Calculate the Perimeter of the Square
The perimeter of a square is calculated using the formula:
[tex]\[ \text{Perimeter} = 4 \times \text{Side length} \][/tex]
So, with the side length determined as 46 meters:
[tex]\[ \text{Perimeter} = 4 \times 46 \][/tex]
[tex]\[ \text{Perimeter} = 184 \, \text{meters} \][/tex]
### Step 3: Calculate the Total Distance Covered in 5 Rounds
If a man takes 5 rounds along the boundary of the square, the total distance covered can be calculated as:
[tex]\[ \text{Total distance covered} = \text{Number of rounds} \times \text{Perimeter} \][/tex]
Given that he takes 5 rounds:
[tex]\[ \text{Total distance covered} = 5 \times 184 \][/tex]
[tex]\[ \text{Total distance covered} = 920 \, \text{meters} \][/tex]
### Final Answer
- The side length of the square plot is 46 meters.
- The perimeter of the square plot is 184 meters.
- The total distance covered by the man in 5 rounds is 920 meters.
