The length of each side of an equilateral triangle having an area of `9 sqrt3 cm^(2)` is

Options

A. 8 cm
B. 36 cm
C. 4 cm
D. 6 cm

Explanation

To find the length of each side of an equilateral triangle given its area, we can use the formula for the area of an equilateral triangle:

\[ \text{Area} = \frac{\sqrt{3}}{4} a^2 \]

where \( a \) is the length of each side of the triangle.

### Step-by-Step Solution:

1. **Set up the equation using the given area**:
We know the area of the triangle is \( 9\sqrt{3} \, \text{cm}^2 \). Therefore, we can write the equation:
\[ \frac{\sqrt{3}}{4} a^2 = 9\sqrt{3} \]

2. **Eliminate \(\sqrt{3}\) from both sides**:
To simplify the equation, we can multiply both sides by \( \frac{4}{\sqrt{3}} \):
\[ a^2 = 9\sqrt{3} \times \frac{4}{\sqrt{3}} \]
This simplifies to:
\[ a^2 = 9 \times 4 = 36 \]

3. **Solve for \( a \)**:
Now, take the square root of both sides:
\[ a = \sqrt{36} = 6 \]

4. **Conclusion**:
The length of each side of the equilateral triangle is \( 6 \, \text{cm} \).

### Final Answer:
The length of each side of the equilateral triangle is \( 6 \, \text{cm} \).