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:

### Step 1: Understand the given information
We know the area \( A \) of the rectangle and the length \( l \). The area of a rectangle is given by the formula:
\[ A = \text{length} \times \text{breadth} \]

### Step 2: Express breadth in terms of area and length
From the area formula, we can express the breadth \( b \) as:
\[ b = \frac{A}{l} \]

### Step 3: Write the formula for the perimeter
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2 \times (\text{length} + \text{breadth}) = 2(l + b) \]

### Step 4: Substitute the expression for breadth into the perimeter formula
Now, we substitute the expression for breadth \( b \) into the perimeter formula:
\[ P = 2 \left( l + \frac{A}{l} \right) \]

### Step 5: Simplify the expression
Distributing the 2 gives us:
\[ P = 2l + 2 \left( \frac{A}{l} \right) \]
This can be rewritten as:
\[ P = 2l + \frac{2A}{l} \]

### Final Answer
Thus, the perimeter of the rectangle is:
\[ P = 2l + \frac{2A}{l} \text{ cm} \]

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