IDNLearn.com is your reliable source for expert answers and community insights. Discover thorough and trustworthy answers from our community of knowledgeable professionals, tailored to meet your specific needs.

9. The area of a square plot is 2116 m². A man takes 5 rounds of the boundary of this plot. Find the distance covered by him.

Sagot :

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.