A man riding a bicycle completes one lap of a square field along its perimeter at the speed of 43.2km/hr in 1 minute 20 seconds . What is the area of the field ?

Options

A. 52900 sq. m
B. 57600 sq m
C. 48400 sq m
D. Cannot be determined

Explanation

To solve the problem step by step, we will follow the logical sequence of calculations based on the information given.

### Step 1: Convert Speed from km/hr to m/s
The speed given is 43.2 km/hr. We need to convert this speed into meters per second (m/s).

1 km = 1000 meters
1 hour = 3600 seconds (60 minutes × 60 seconds)

To convert km/hr to m/s, we use the formula:
\[ \text{Speed in m/s} = \text{Speed in km/hr} \times \frac{1000 \text{ m}}{3600 \text{ s}} \]

Calculating:
\[ \text{Speed in m/s} = 43.2 \times \frac{1000}{3600} = 12 \text{ m/s} \]

### Step 2: Convert Time from Minutes and Seconds to Seconds
The time taken to complete one lap is given as 1 minute 20 seconds. We need to convert this time into seconds.

1 minute = 60 seconds
So,
\[ \text{Total time in seconds} = 1 \text{ minute} + 20 \text{ seconds} = 60 + 20 = 80 \text{ seconds} \]

### Step 3: Calculate the Total Distance Covered
The total distance covered in one lap can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Using the values we have:
\[ \text{Distance} = 12 \text{ m/s} \times 80 \text{ s} = 960 \text{ meters} \]

### Step 4: Determine the Perimeter of the Square Field
Since the man completes one lap along the perimeter of the square field, the perimeter \( P \) is equal to the total distance covered.
Thus,
\[ P = 960 \text{ meters} \]

### Step 5: Calculate the Side Length of the Square
The perimeter of a square is given by the formula:
\[ P = 4 \times \text{side} \]

We can rearrange this to find the side length:
\[ \text{side} = \frac{P}{4} = \frac{960}{4} = 240 \text{ meters} \]

### Step 6: Calculate the Area of the Square Field
The area \( A \) of a square is given by the formula:
\[ A = \text{side}^2 \]

Calculating the area:
\[ A = 240^2 = 57600 \text{ square meters} \]

### Final Answer
The area of the field is \( 57600 \text{ m}^2 \).

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