The perimeter and the breadth of a rectangle are 60 cm and 14 cm respectively. Find its area (in `cm^2`).

Options

A. 112
B. 448
C. 224
D. 336

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

### Step 2: Substitute the known values into the perimeter formula.
We know the perimeter \( P = 60 \, \text{cm} \) and the breadth \( B = 14 \, \text{cm} \). Substituting these values into the perimeter formula gives:
\[ 60 = 2 \times (L + 14) \]

### Step 3: Simplify the equation to find the length \( L \).
First, divide both sides of the equation by 2:
\[ 30 = L + 14 \]
Next, subtract 14 from both sides to isolate \( L \):
\[ L = 30 - 14 = 16 \, \text{cm} \]

### 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:
\[ A = 16 \times 14 \]

### Step 5: Perform the multiplication to find the area.
Calculating the area:
\[ A = 16 \times 14 = 224 \, \text{cm}^2 \]

### Final Answer:
The area of the rectangle is \( 224 \, \text{cm}^2 \).

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