The perimeter of a square is thrice the perimeter of R rectangle. If the perimeter of the square is 84 cm and tllc length of the rectangle is 8 cm, what is the difference between the breadth of the rectangle and the side of the square?

Options

A. 15 cm
B. 19 cm
C. 10 cm
D. 8 cm

Explanation

To solve the problem step by step, we need to find the difference between the breadth of the rectangle and the side of the square.

### Step 1: Understand the given information
- The perimeter of the square is 84 cm.
- The length of the rectangle is 8 cm.
- The perimeter of the square is thrice the perimeter of the rectangle.

### Step 2: Calculate the perimeter of the rectangle
Let the breadth of the rectangle be \( b \). The formula for the perimeter of a rectangle is:
\[ \text{Perimeter of rectangle} = 2 \times (\text{Length} + \text{Breadth}) = 2 \times (8 + b) \]

### Step 3: Set up the equation
According to the problem, the perimeter of the square is thrice the perimeter of the rectangle. Therefore, we can write:
\[ 84 = 3 \times (2 \times (8 + b)) \]

### Step 4: Simplify the equation
First, simplify the right side:
\[ 84 = 3 \times (16 + 2b) \]
\[ 84 = 48 + 6b \]

### Step 5: Solve for \( b \)
Now, isolate \( b \):
\[ 84 - 48 = 6b \]
\[ 36 = 6b \]
\[ b = \frac{36}{6} = 6 \text{ cm} \]

### Step 6: Find the side of the square
The side of the square can be calculated from its perimeter:
\[ \text{Perimeter of square} = 4 \times \text{side} \]
\[ 84 = 4 \times \text{side} \]
\[ \text{side} = \frac{84}{4} = 21 \text{ cm} \]

### Step 7: Calculate the difference
Now, we need to find the difference between the breadth of the rectangle and the side of the square:
\[ \text{Difference} = \text{side of square} - \text{breadth of rectangle} = 21 - 6 = 15 \text{ cm} \]

### Final Answer
The difference between the breadth of the rectangle and the side of the square is \( 15 \text{ cm} \).

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