The area of an equilateral triangle is `18sqrt(3)` sq. units. Find the value of side (in units) of the tri angle.

Options

A. `sqrt(2)`
B. `2sqrt(2)`
C. `3sqrt(2)`
D. `6sqrt(2)`

Answer

To find the side length 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 1: Set up the equation
We know the area of the triangle is given as \( 18\sqrt{3} \) square units. Therefore, we can set up the equation:

\[ \frac{\sqrt{3}}{4} a^2 = 18\sqrt{3} \]

### Step 2: Eliminate \(\sqrt{3}\)
To simplify the equation, we can divide both sides by \(\sqrt{3}\):

\[ \frac{1}{4} a^2 = 18 \]

### Step 3: Multiply by 4
Next, we multiply both sides by 4 to isolate \( a^2 \):

\[ a^2 = 18 \times 4 \]

### Step 4: Calculate \( 18 \times 4 \)
Calculating the right side gives us:

\[ a^2 = 72 \]

### Step 5: Take the square root
Now, we take the square root of both sides to find \( a \):

\[ a = \sqrt{72} \]

### Step 6: Simplify \( \sqrt{72} \)
We can simplify \( \sqrt{72} \):

\[ \sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2} \]

### Conclusion
Thus, the length of the side of the equilateral triangle is:

\[ a = 6\sqrt{2} \text{ units} \]