The area of a rectangular field is `3584 m^(2)` and its length is 64 m. A boy runs around the field at the rate of 6 km//h. How long will he take to go 5 times around it?

Answer

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

### Step 1: Find the breadth of the rectangular field.
We know that the area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]

Given:
- Area = \( 3584 \, m^2 \)
- Length = \( 64 \, m \)

We can rearrange the formula to find the breadth:
\[ \text{Breadth} = \frac{\text{Area}}{\text{Length}} \]
\[ \text{Breadth} = \frac{3584}{64} = 56 \, m \]

### Step 2: Calculate the perimeter of the rectangular field.
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2 \times (\text{Length} + \text{Breadth}) \]

Substituting the values we have:
\[ P = 2 \times (64 + 56) \]
\[ P = 2 \times 120 = 240 \, m \]

### Step 3: Calculate the distance the boy runs in 5 rounds.
If the boy runs around the field 5 times, the total distance \( D \) he runs is:
\[ D = 5 \times P \]
\[ D = 5 \times 240 = 1200 \, m \]

### Step 4: Convert the distance from meters to kilometers.
Since the boy's speed is given in kilometers per hour, we need to convert the distance from meters to kilometers:
\[ D = \frac{1200}{1000} = 1.2 \, km \]

### Step 5: Calculate the time taken to run 1.2 km at a speed of 6 km/h.
We know that time \( t \) can be calculated using the formula:
\[ t = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values:
\[ t = \frac{1.2 \, km}{6 \, km/h} \]
\[ t = 0.2 \, h \]

### Step 6: Convert time from hours to minutes.
To convert hours to minutes, we multiply by 60:
\[ t = 0.2 \times 60 = 12 \, minutes \]

### Final Answer:
The boy will take **12 minutes** to run 5 times around the field.

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