The breadth of a rectangular plot is `1/5`th of the length of the plot. Inside the plot a garden with an area of `15m^2` is constructed occupying `1/3`rd of the area of the plot. What is the perimeter of the rectangular plot?

Options

A. 42 metres
B. 72 metres
C. 48 metres
D. 36 metres

Answer

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

### Step 1: Define Variables
Let the length of the rectangular plot be \( L \) and the breadth be \( B \). According to the problem, the breadth is \( \frac{1}{5} \) of the length. Therefore, we can express this relationship as:
\[ B = \frac{1}{5} L \]

### Step 2: Area of the Plot
The area of a rectangle is given by the formula:
\[ \text{Area} = L \times B \]
Substituting the expression for breadth, we have:
\[ \text{Area} = L \times \left(\frac{1}{5} L\right) = \frac{1}{5} L^2 \]

### Step 3: Area of the Garden
We know that the area of the garden is \( 15 \, m^2 \) and it occupies \( \frac{1}{3} \) of the area of the plot. Therefore, we can set up the equation:
\[ 15 = \frac{1}{3} \times \text{Area of the plot} \]
This implies:
\[ \text{Area of the plot} = 15 \times 3 = 45 \, m^2 \]

### Step 4: Set Up the Equation
Now we can equate the area of the plot calculated in Step 2 to the area found in Step 3:
\[ \frac{1}{5} L^2 = 45 \]

### Step 5: Solve for Length
To find \( L^2 \), we multiply both sides by 5:
\[ L^2 = 45 \times 5 = 225 \]
Now, taking the square root of both sides gives us:
\[ L = \sqrt{225} = 15 \, m \]

### Step 6: Find the Breadth
Using the relationship between length and breadth from Step 1:
\[ B = \frac{1}{5} L = \frac{1}{5} \times 15 = 3 \, m \]

### Step 7: Calculate the Perimeter
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2(L + B) \]
Substituting the values of \( L \) and \( B \):
\[ P = 2(15 + 3) = 2 \times 18 = 36 \, m \]

### Final Answer
The perimeter of the rectangular plot is \( 36 \, m \).

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