The length of a rectangle is 16 cm and its perimeter is equal to the perimeter of a square with side 12.5 cm. Find the area of the rectangle.

Answer

To find the area of the rectangle, we will follow these steps:

### Step 1: Understand the problem
We know the length of the rectangle and the perimeter of the rectangle is equal to the perimeter of a square with a given side length.

### Step 2: Write down the given information
- Length of the rectangle (l) = 16 cm
- Side of the square (s) = 12.5 cm

### Step 3: Calculate the perimeter of the square
The formula for the perimeter of a square is:
\[ \text{Perimeter of square} = 4 \times \text{side} \]
Substituting the value of the side:
\[ \text{Perimeter of square} = 4 \times 12.5 = 50 \text{ cm} \]

### Step 4: Set up the equation for the perimeter of the rectangle
The formula for the perimeter of a rectangle is:
\[ \text{Perimeter of rectangle} = 2 \times (\text{length} + \text{breadth}) \]
Let the breadth of the rectangle be \( b \). Therefore, we can write:
\[ 2 \times (16 + b) = 50 \]

### Step 5: Solve for the breadth (b)
First, simplify the equation:
\[ 16 + b = \frac{50}{2} \]
\[ 16 + b = 25 \]
Now, isolate \( b \):
\[ b = 25 - 16 \]
\[ b = 9 \text{ cm} \]

### Step 6: Calculate the area of the rectangle
The formula for the area of a rectangle is:
\[ \text{Area} = \text{length} \times \text{breadth} \]
Substituting the values we have:
\[ \text{Area} = 16 \times 9 = 144 \text{ cm}^2 \]

### Final Answer
The area of the rectangle is \( 144 \text{ cm}^2 \).

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