Area of a square is same as that of a rectangle. The length and the breadth of the rectangle are respectively 5 cm more and 4 cm less than the side of the square. Find the side of the square.

Answer

To solve the problem step by step, we will follow the mathematical reasoning laid out in the video transcript.

### Step-by-Step Solution:

1. **Understand the Problem Statement**:
We know that the area of a square is equal to the area of a rectangle. The length of the rectangle is 5 cm more than the side of the square, and the breadth of the rectangle is 4 cm less than the side of the square.

2. **Define Variables**:
Let the side of the square be denoted as \( s \) cm.

3. **Write the Area Formulas**:
- The area of the square is given by:
\[ \text{Area of square} = s \times s = s^2 \]
- The length \( L \) of the rectangle is:
\[ L = s + 5 \]
- The breadth \( B \) of the rectangle is:
\[ B = s - 4 \]
- The area of the rectangle is given by:
\[ \text{Area of rectangle} = L \times B = (s + 5)(s - 4) \]

4. **Set the Areas Equal**:
Since the area of the square is equal to the area of the rectangle, we can write:
\[ s^2 = (s + 5)(s - 4) \]

5. **Expand the Right Side**:
Now, we will expand the right-hand side:
\[ (s + 5)(s - 4) = s^2 - 4s + 5s - 20 = s^2 + s - 20 \]

6. **Formulate the Equation**:
Now we have:
\[ s^2 = s^2 + s - 20 \]

7. **Simplify the Equation**:
Subtract \( s^2 \) from both sides:
\[ 0 = s - 20 \]

8. **Solve for \( s \)**:
Rearranging gives:
\[ s = 20 \]

9. **Conclusion**:
Therefore, the side of the square is \( 20 \) cm.