The perimeter of a rectangle having area equal to 144 cm and sides in the ratio`4:9` is

Options

A. 52 cm
B. 56 cm
C. 60 cm
D. 64 cm

Answer

To solve the problem, we need to find the perimeter of a rectangle whose area is given as 144 cm² and whose sides are in the ratio of 4:9.

### Step-by-Step Solution:

1. **Understanding the Ratio**:
- The sides of the rectangle are in the ratio 4:9. Let's denote the length (L) and breadth (B) of the rectangle as:
- Length (L) = 4x
- Breadth (B) = 9x
- Here, 'x' is a common multiplier.

2. **Using the Area Formula**:
- The area (A) of a rectangle is given by the formula:
\[ A = L \times B \]
- Substituting the expressions for L and B:
\[ A = (4x) \times (9x) = 36x^2 \]

3. **Setting Up the Equation**:
- We know the area is 144 cm², so we can set up the equation:
\[ 36x^2 = 144 \]

4. **Solving for x**:
- To find 'x', divide both sides of the equation by 36:
\[ x^2 = \frac{144}{36} = 4 \]
- Taking the square root of both sides:
\[ x = \sqrt{4} = 2 \]

5. **Finding Length and Breadth**:
- Now, substitute the value of 'x' back into the expressions for length and breadth:
- Length (L) = 4x = 4(2) = 8 cm
- Breadth (B) = 9x = 9(2) = 18 cm

6. **Calculating the Perimeter**:
- The perimeter (P) of a rectangle is given by the formula:
\[ P = 2(L + B) \]
- Substituting the values of L and B:
\[ P = 2(8 + 18) = 2(26) = 52 \text{ cm} \]

### Final Answer:
The perimeter of the rectangle is **52 cm**.