Radhika runs along the boundary of a rectangular park at the rate of 12 km/hr and completes one full round in 15 minutes.If the length of the park is 4 times its breadth , the area of the park is -----

Options

A. A)`360000 m^2`
B. B)`36000 m^2`
C. C)`3600 m^2`
D. D)None of these

Answer

To solve the problem step by step, we will follow the information provided in the question and use the relationships between the dimensions of the rectangular park.

### Step 1: Determine the distance Radhika runs in one round
Radhika runs at a speed of 12 km/hr and completes one round in 15 minutes. First, we need to convert the time from minutes to hours.

\[ \text{Time in hours} = \frac{15 \text{ minutes}}{60} = \frac{1}{4} \text{ hours} \]

Now, we can calculate the distance she runs in one round using the formula:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Substituting the values:

\[ \text{Distance} = 12 \text{ km/hr} \times \frac{1}{4} \text{ hr} = 3 \text{ km} \]

### Step 2: Relate the distance to the perimeter of the park
The distance Radhika runs in one round is equal to the perimeter of the rectangular park. The perimeter \( P \) of a rectangle is given by:

\[ P = 2(\text{Length} + \text{Breadth}) \]

Let the breadth be \( k \) meters. Since the length is 4 times the breadth, the length will be \( 4k \) meters. Therefore, the perimeter can be expressed as:

\[ P = 2(k + 4k) = 2(5k) = 10k \]

Setting this equal to the distance Radhika runs:

\[ 10k = 3 \text{ km} = 3000 \text{ meters} \]

### Step 3: Solve for the breadth \( k \)
Now we can solve for \( k \):

\[ k = \frac{3000 \text{ meters}}{10} = 300 \text{ meters} \]

### Step 4: Calculate the length of the park
Since the length is 4 times the breadth:

\[ \text{Length} = 4k = 4 \times 300 = 1200 \text{ meters} \]

### Step 5: Calculate the area of the park
The area \( A \) of a rectangle is given by:

\[ A = \text{Length} \times \text{Breadth} \]

Substituting the values we found:

\[ A = 1200 \text{ meters} \times 300 \text{ meters} = 360000 \text{ square meters} \]

### Conclusion
The area of the park is:

\[ \text{Area} = 360000 \text{ square meters} \]