The length of a rectangular plot of ground is four times its breadth and its area is 4 hectares . How long will it take to a dog to walk round it at the rate of 3 km/hr ?

Options

A. 12 min
B. 20 min
C. 21 min
D. 18.5 min

Answer

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

### Step 1: Understand the dimensions of the rectangular plot
Let the breadth of the rectangular plot be \( b \). According to the problem, the length \( l \) is four times the breadth:
\[ l = 4b \]

### Step 2: Use the area to find the dimensions
The area \( A \) of a rectangle is given by the formula:
\[ A = l \times b \]
We know the area is 4 hectares. Since 1 hectare is equal to 10,000 square meters, we convert 4 hectares to square meters:
\[ A = 4 \times 10,000 = 40,000 \text{ m}^2 \]

Now substituting the expression for length:
\[ 40,000 = (4b) \times b \]
\[ 40,000 = 4b^2 \]

### Step 3: Solve for breadth
To find \( b \), we can rearrange the equation:
\[ b^2 = \frac{40,000}{4} \]
\[ b^2 = 10,000 \]
Taking the square root of both sides:
\[ b = 100 \text{ m} \]

### Step 4: Find the length
Now we can find the length \( l \):
\[ l = 4b = 4 \times 100 = 400 \text{ m} \]

### Step 5: Calculate the perimeter
The perimeter \( P \) of a rectangle is given by:
\[ P = 2(l + b) \]
Substituting the values of \( l \) and \( b \):
\[ P = 2(400 + 100) = 2 \times 500 = 1000 \text{ m} \]

### Step 6: Calculate the time taken to walk around the plot
The dog walks at a speed of 3 km/hr. First, we convert this speed to meters per minute:
\[ 3 \text{ km/hr} = 3000 \text{ m/hr} = \frac{3000}{60} \text{ m/min} = 50 \text{ m/min} \]

Now, we can find the time \( t \) taken to walk around the perimeter:
\[ t = \frac{P}{\text{speed}} = \frac{1000 \text{ m}}{50 \text{ m/min}} = 20 \text{ minutes} \]

### Final Answer
It will take the dog **20 minutes** to walk around the rectangular plot.

---