The area of a rectangle is `A cm ^(2)` and length is l cm. Its perimeter (in cm ) is

Options

A. `2 l + (A)/(l)`
B. `2 l + (2A)/( l)`
C. `2l + 2A `
D. `2 l + (A)/(2l)`

Answer

To find the perimeter of a rectangle given its area and length, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The area of the rectangle is \( A \) cm².
- The length of the rectangle is \( l \) cm.

2. **Use the Formula for Area**:
- The area \( A \) of a rectangle is calculated using the formula:
\[ A = \text{length} \times \text{breadth} \]
- Substituting the known values:
\[ A = l \times b \]
- Here, \( b \) is the breadth of the rectangle.

3. **Solve for Breadth**:
- Rearranging the formula to find the breadth \( b \):
\[ b = \frac{A}{l} \]

4. **Use the Formula for Perimeter**:
- The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2 \times (\text{length} + \text{breadth}) \]
- Substituting the values we have:
\[ P = 2 \times \left(l + b\right) \]

5. **Substitute the Value of Breadth**:
- Now substitute \( b \) with \( \frac{A}{l} \):
\[ P = 2 \times \left(l + \frac{A}{l}\right) \]

6. **Simplify the Expression**:
- Distributing the 2:
\[ P = 2l + 2 \times \frac{A}{l} \]
- Therefore, the final expression for the perimeter is:
\[ P = 2l + \frac{2A}{l} \]

### Final Answer:
The perimeter of the rectangle is \( 2l + \frac{2A}{l} \) cm.

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