A square playground measures 1127.6164 sq. m. If a man walks `2 (9)/(20)` m a minute, the time taken by him to walk one round around it is approximately

Options

A. a)50.82 min
B. b)54.82 min
C. c)54.62 min
D. d)50.62 min

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Find the side length of the square playground.
The area of the square playground is given as 1127.6164 sq. m. The formula for the area of a square is:
\[ \text{Area} = \text{side}^2 \]
To find the side length, we take the square root of the area:
\[ \text{side} = \sqrt{1127.6164} \]

### Step 2: Calculate the square root.
Using the long division method or a calculator, we find:
\[ \text{side} \approx 33.58 \text{ m} \]

### Step 3: Calculate the perimeter of the square playground.
The perimeter \( P \) of a square is given by:
\[ P = 4 \times \text{side} \]
Substituting the value of the side:
\[ P = 4 \times 33.58 \approx 134.32 \text{ m} \]

### Step 4: Convert the speed from mixed fraction to improper fraction.
The speed of the man is given as \( 2 \frac{9}{20} \) m/min. To convert this to an improper fraction:
\[ 2 \frac{9}{20} = \frac{2 \times 20 + 9}{20} = \frac{40 + 9}{20} = \frac{49}{20} \text{ m/min} \]

### Step 5: Calculate the time taken to walk one round.
The time \( t \) taken to walk the perimeter can be calculated using the formula:
\[ t = \frac{\text{Distance}}{\text{Speed}} \]
Substituting the values we have:
\[ t = \frac{134.32}{\frac{49}{20}} = 134.32 \times \frac{20}{49} \]

### Step 6: Perform the multiplication and division.
Calculating the above expression:
\[ t = \frac{134.32 \times 20}{49} \approx \frac{2686.4}{49} \approx 54.82 \text{ minutes} \]

### Final Answer:
The time taken by the man to walk one round around the playground is approximately **54.82 minutes**.

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