The area of a rectangle is `27 m^(2)` and is length is thrice its breadth. The perimeter of rectangle is :

Options

A. a)28 cm
B. b)42 cm
C. c)12 cm
D. d)24 cm

Answer

To find the perimeter of the rectangle given that its area is \(27 \, m^2\) and its length is thrice its breadth, we can follow these steps:

### Step 1: Define the variables
Let the breadth of the rectangle be \(x\). Since the length is thrice the breadth, we can express the length as:
\[ \text{Length} = 3x \]

### Step 2: Use the area formula
The area \(A\) of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Breadth} \]
Substituting the values we have:
\[ 27 = 3x \times x \]
This simplifies to:
\[ 27 = 3x^2 \]

### Step 3: Solve for \(x\)
To find \(x\), we can rearrange the equation:
\[ x^2 = \frac{27}{3} \]
\[ x^2 = 9 \]
Taking the square root of both sides, we find:
\[ x = 3 \]

### Step 4: Find the length
Now that we have the breadth, we can find the length:
\[ \text{Length} = 3x = 3 \times 3 = 9 \]

### Step 5: Calculate the perimeter
The perimeter \(P\) of a rectangle is given by the formula:
\[ P = 2 \times (\text{Length} + \text{Breadth}) \]
Substituting the values we found:
\[ P = 2 \times (9 + 3) = 2 \times 12 = 24 \]

### Final Answer
The perimeter of the rectangle is:
\[ \boxed{24 \, m} \]

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