The perimeter and the breadth of a rectangle are 52 cm and 12 cm respectively. Find its area (in `cm^(2)`).

Options

A. 84
B. 336
C. 168
D. 252

Answer

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

### Step 1: Understand the formula for the perimeter of a rectangle.
The formula for the perimeter (P) of a rectangle is given by:
\[ P = 2 \times (L + B) \]
where \( L \) is the length and \( B \) is the breadth.

### Step 2: Substitute the known values into the perimeter formula.
We know that the perimeter is 52 cm and the breadth is 12 cm. Therefore, we can write:
\[ 52 = 2 \times (L + 12) \]

### Step 3: Solve for the length (L).
First, divide both sides of the equation by 2:
\[ 26 = L + 12 \]
Now, subtract 12 from both sides to find the length:
\[ L = 26 - 12 \]
\[ L = 14 \text{ cm} \]

### Step 4: Calculate the area of the rectangle.
The area (A) of a rectangle is calculated using the formula:
\[ A = L \times B \]
Substituting the values we found:
\[ A = 14 \times 12 \]

### Step 5: Perform the multiplication.
Now, calculate the area:
\[ A = 168 \text{ cm}^2 \]

### Final Answer:
The area of the rectangle is \( 168 \text{ cm}^2 \).

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