A rectangle has a perimeter of 72 cm. If its length is 20 cm then area of the rectangle in square centimetres is

Options

A. 400
B. 320
C. 3200
D. 36

Answer

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

### Step 1: Understand the formula for the perimeter of a rectangle.
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2 \times (\text{Length} + \text{Breadth}) \]

### Step 2: Substitute the known values into the perimeter formula.
We know the perimeter \( P = 72 \) cm and the length \( L = 20 \) cm. Substituting these values into the formula:
\[ 72 = 2 \times (20 + \text{Breadth}) \]

### Step 3: Simplify the equation.
First, divide both sides by 2:
\[ 36 = 20 + \text{Breadth} \]

### Step 4: Solve for the breadth.
Now, subtract 20 from both sides to find the breadth:
\[ \text{Breadth} = 36 - 20 = 16 \text{ cm} \]

### Step 5: Calculate the area of the rectangle.
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Breadth} \]
Substituting the values we have:
\[ A = 20 \times 16 \]

### Step 6: Perform the multiplication.
Calculating the area:
\[ A = 320 \text{ cm}^2 \]

### Final Answer:
The area of the rectangle is \( 320 \text{ cm}^2 \).

---