In a square ABCD, AB = (4x + 3) cm and BC = (5x - 6) cm. Then, the value of x is

Answer

To solve the problem, we need to find the value of \( x \) given that in a square \( ABCD \), the lengths of sides \( AB \) and \( BC \) are expressed as \( AB = (4x + 3) \) cm and \( BC = (5x - 6) \) cm.

### Step-by-Step Solution:

1. **Understand the properties of a square**:
In a square, all sides are equal. Therefore, we can set the lengths of sides \( AB \) and \( BC \) equal to each other.

\[ AB = BC \]

2. **Set up the equation**:
Substitute the expressions for \( AB \) and \( BC \) into the equation:

\[ 4x + 3 = 5x - 6 \]

3. **Rearrange the equation**:
To isolate \( x \), we will move all terms involving \( x \) to one side and constant terms to the other side. Subtract \( 4x \) from both sides:

\[ 3 = 5x - 4x - 6 \]

Simplifying this gives:

\[ 3 = x - 6 \]

4. **Solve for \( x \)**:
Now, add \( 6 \) to both sides to solve for \( x \):

\[ 3 + 6 = x \]

\[ x = 9 \]

5. **Conclusion**:
The value of \( x \) is \( 9 \).