If the area of a rectangle is equal to the area of a square and length of the rectangle is equal to the perimeter of the square, then the breadth of rectangle is ____

Options

A. Side +2
B. `("Side")^(2) +2`
C. Side `div 4`
D. Side `div 3`

Answer

To solve the problem, we need to establish the relationship between the rectangle and the square based on the information given.

### Step-by-Step Solution:

1. **Define the variables:**
Let the side of the square be \( s \).
The area of the square is given by:
\[ \text{Area of square} = s^2 \]

2. **Establish the area of the rectangle:**
Let the length of the rectangle be \( l \) and the breadth be \( b \).
The area of the rectangle is given by:
\[ \text{Area of rectangle} = l \times b \]

3. **Set the areas equal:**
According to the problem, the area of the rectangle is equal to the area of the square:
\[ l \times b = s^2 \]

4. **Define the perimeter of the square:**
The perimeter \( P \) of the square is given by:
\[ P = 4s \]

5. **Set the length of the rectangle equal to the perimeter of the square:**
According to the problem, the length of the rectangle is equal to the perimeter of the square:
\[ l = 4s \]

6. **Substitute the value of \( l \) in the area equation:**
Substitute \( l = 4s \) into the area equation:
\[ 4s \times b = s^2 \]

7. **Solve for \( b \):**
To find \( b \), divide both sides of the equation by \( 4s \):
\[ b = \frac{s^2}{4s} \]
Simplifying this gives:
\[ b = \frac{s}{4} \]

### Final Answer:
The breadth of the rectangle is \( \frac{s}{4} \).