Area of a rectangle is equal to the urea of the circle whose radius is 21 cms. If the length and the breadth of the rectangle are in the ratio of 14 : 11 res peetively, what is its perimeter ?

Options

A. 142 cms.
B. 140 cms.
C. 132 cms.
D. 150 cms.

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Calculate the area of the circle
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius. Here, the radius is given as 21 cm.

Substituting the radius into the formula:
\[ A = \pi (21)^2 = \pi \times 441 \]
Using \( \pi \approx 3.14 \):
\[ A \approx 3.14 \times 441 \approx 1385.94 \text{ cm}^2 \]
For simplicity, we can round this to:
\[ A \approx 1386 \text{ cm}^2 \]

### Step 2: Set up the ratio for length and breadth
The length \( L \) and breadth \( B \) of the rectangle are in the ratio of 14:11. We can express them as:
\[ L = 14x \quad \text{and} \quad B = 11x \]

### Step 3: Write the equation for the area of the rectangle
The area of the rectangle is given by:
\[ \text{Area} = L \times B = (14x) \times (11x) = 154x^2 \]
Since the area of the rectangle is equal to the area of the circle, we have:
\[ 154x^2 = 1386 \]

### Step 4: Solve for \( x^2 \)
To find \( x^2 \), we divide both sides by 154:
\[ x^2 = \frac{1386}{154} \]
Calculating the right side:
\[ x^2 = 9 \]
Taking the square root of both sides gives:
\[ x = 3 \]

### Step 5: Calculate the length and breadth
Now we can find the length and breadth:
\[ L = 14x = 14 \times 3 = 42 \text{ cm} \]
\[ B = 11x = 11 \times 3 = 33 \text{ cm} \]

### Step 6: Calculate the perimeter of the rectangle
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2(L + B) \]
Substituting the values of \( L \) and \( B \):
\[ P = 2(42 + 33) = 2 \times 75 = 150 \text{ cm} \]

### Final Answer:
The perimeter of the rectangle is \( 150 \text{ cm} \).

---