The area of an equilateral triangle is `9 sqrt(3) cm^(2)` . Find its side (in cm).

Options

A. 3
B. 6
C. 12
D. 18

Answer

To find the 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 a side of the triangle.

### Step-by-Step Solution:

1. **Set the area equal to the given value**:
Given that the area of the triangle is \( 9\sqrt{3} \, \text{cm}^2 \), we can set up the equation:
\[ \frac{\sqrt{3}}{4} a^2 = 9\sqrt{3} \]

2. **Eliminate \(\sqrt{3}\) from both sides**:
To simplify, we can divide both sides of the equation by \(\sqrt{3}\):
\[ \frac{1}{4} a^2 = 9 \]

3. **Multiply both sides by 4**:
To isolate \( a^2 \), multiply both sides by 4:
\[ a^2 = 36 \]

4. **Take the square root of both sides**:
To find \( a \), take the square root of both sides:
\[ a = \sqrt{36} \]
\[ a = 6 \, \text{cm} \]

Thus, the length of each side of the equilateral triangle is \( 6 \, \text{cm} \).

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

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