The perimeter of a rectangle is 200 cm and its breadth is 36 cm. Find the area of the rectangle.

Options

A. `7200 cm^(2)`
B. `2304 cm^(2)`
C. `360 cm^(2)`
D. `18040 cm^(2)`

Answer

To solve the problem step by step, we will 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:
\[ P = 2(L + B) \]
where \( L \) is the length and \( B \) is the breadth.

### Step 2: Substitute the known values into the perimeter formula.
We know the perimeter \( P \) is 200 cm and the breadth \( B \) is 36 cm. We can substitute these values into the formula:
\[ 200 = 2(L + 36) \]

### Step 3: Simplify the equation to find the length.
First, divide both sides of the equation by 2:
\[ 100 = L + 36 \]
Next, isolate \( L \) by subtracting 36 from both sides:
\[ L = 100 - 36 \]
\[ L = 64 \text{ cm} \]

### Step 4: Calculate the area of the rectangle.
Now that we have both the length and the breadth, we can find the area \( A \) using the formula:
\[ A = L \times B \]
Substituting the values we found:
\[ A = 64 \times 36 \]

### Step 5: Perform the multiplication to find the area.
Calculating \( 64 \times 36 \):
\[ A = 2304 \text{ cm}^2 \]

### Final Answer:
The area of the rectangle is \( 2304 \text{ cm}^2 \).

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