An acute angle made by a side of parallelogram with other pair of parallel side is `60^(@)` . If the distance between these parallel sides is ` 6 sqrt(3)` , the other side is :

Options

A. `12 cm `
B. `12 sqrt(3) cm `
C. `15 sqrt(3) cm `
D. none of these

Answer

To solve the problem, we need to find the length of the other side of the parallelogram given that the acute angle made by one side with the other pair of parallel sides is \(60^\circ\) and the distance between these parallel sides is \(6\sqrt{3}\).

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The acute angle \( \theta = 60^\circ \)
- The distance between the parallel sides (height) \( h = 6\sqrt{3} \)

2. **Use the Definition of Sine:**
In a right triangle, the sine of an angle is defined as:
\[ \sin(\theta) = \frac{\text{Opposite Side}}{\text{Hypotenuse}} \]
Here, the opposite side corresponds to the height \( h \) and the hypotenuse corresponds to the length of the side of the parallelogram we want to find, which we will denote as \( a \).

3. **Set Up the Equation:**
For \( \theta = 60^\circ \):
\[ \sin(60^\circ) = \frac{h}{a} \]
We know that \( \sin(60^\circ) = \frac{\sqrt{3}}{2} \). Plugging in the values:
\[ \frac{\sqrt{3}}{2} = \frac{6\sqrt{3}}{a} \]

4. **Cross-Multiply to Solve for \( a \):**
\[ \sqrt{3} \cdot a = 2 \cdot 6\sqrt{3} \]
Simplifying the right side:
\[ \sqrt{3} \cdot a = 12\sqrt{3} \]

5. **Divide Both Sides by \( \sqrt{3} \):**
\[ a = \frac{12\sqrt{3}}{\sqrt{3}} = 12 \]

6. **Conclusion:**
The length of the other side of the parallelogram is \( 12 \) cm.

### Final Answer:
The other side of the parallelogram is \( 12 \) cm.