The perimeter of a square is twice the perimeter of a rectangle. If the perimeter of the square is 56 cm and the length of the rectangle is 9 cm, what is the difference between the breadth of the rectangle and the side of the square?

Options

A. 7 cm
B. 9 cm
C. 11 cm
D. 5 cm

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the relationship between the perimeters
The problem states that the perimeter of a square is twice the perimeter of a rectangle.

### Step 2: Calculate the side of the square
The perimeter of a square (P_square) is given as 56 cm. The formula for the perimeter of a square is:
\[ P_{square} = 4 \times \text{side} \]
So, we can find the side of the square:
\[ \text{side} = \frac{P_{square}}{4} = \frac{56}{4} = 14 \text{ cm} \]

### Step 3: Calculate the perimeter of the rectangle
Since the perimeter of the square is twice the perimeter of the rectangle (P_rectangle), we can write:
\[ P_{rectangle} = \frac{P_{square}}{2} = \frac{56}{2} = 28 \text{ cm} \]

### Step 4: Use the perimeter formula for the rectangle
The formula for the perimeter of a rectangle is:
\[ P_{rectangle} = 2 \times (\text{length} + \text{breadth}) \]
We know the length of the rectangle is given as 9 cm. Thus, we can set up the equation:
\[ 2 \times (9 + b) = 28 \]

### Step 5: Solve for the breadth of the rectangle
Now, we simplify the equation:
\[ 9 + b = \frac{28}{2} = 14 \]
Subtracting 9 from both sides gives:
\[ b = 14 - 9 = 5 \text{ cm} \]

### Step 6: Find the difference between the breadth of the rectangle and the side of the square
Now, we need to find the difference between the breadth of the rectangle and the side of the square:
\[ \text{Difference} = \text{side of square} - \text{breadth of rectangle} = 14 - 5 = 9 \text{ cm} \]

### Final Answer
The difference between the breadth of the rectangle and the side of the square is **9 cm**.

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