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

Options

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

Answer

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

1. **Understand the formula for the area of a rectangle**:
The area \( A \) of a rectangle is given by the formula:
\[ A = l \times w \]
where \( l \) is the length and \( w \) is the width.

2. **Express the width in terms of area and length**:
Rearranging the area formula to solve for width \( w \):
\[ w = \frac{A}{l} \]

3. **Use the formula for the perimeter of a rectangle**:
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2l + 2w \]

4. **Substitute the expression for width into the perimeter formula**:
Now, substitute \( w \) from step 2 into the perimeter formula:
\[ P = 2l + 2\left(\frac{A}{l}\right) \]

5. **Simplify the expression**:
This simplifies to:
\[ P = 2l + \frac{2A}{l} \]

6. **Final expression for the perimeter**:
Therefore, the perimeter of the rectangle is:
\[ P = 2l + \frac{2A}{l} \]

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

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