In a square ABCD, AB=(2x+3) cm and BC=(3x-5) cm . Then , the value of x is

Options

A. 4
B. 5
C. 6
D. 8

Answer

To solve the problem, we need to find the value of \( x \) in the given square ABCD where the lengths of sides AB and BC are given as \( AB = (2x + 3) \) cm and \( BC = (3x - 5) \) 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.

\[ 2x + 3 = 3x - 5 \]

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

\[ 2x + 3 + 5 = 3x \]

This simplifies to:

\[ 2x + 8 = 3x \]

4. **Isolate \( x \)**: Now, subtract \( 2x \) from both sides of the equation.

\[ 8 = 3x - 2x \]

This simplifies to:

\[ 8 = x \]

5. **Conclusion**: Thus, the value of \( x \) is:

\[ x = 8 \]

### Final Answer:
The value of \( x \) is \( 8 \).

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