The area of an equilateral triangle is `36 sqrt3 cm^(2) .` Find its side (in cm).

Options

A. 6
B. 24
C. 12
D. 36

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 the side of the triangle.

### Step-by-Step Solution:

1. **Write down the area formula**:
The area \( A \) of an equilateral triangle is given by:
\[ A = \frac{\sqrt{3}}{4} a^2 \]

2. **Substitute the given area**:
We know the area is \( 36\sqrt{3} \) cm². Therefore, we can set up the equation:
\[ 36\sqrt{3} = \frac{\sqrt{3}}{4} a^2 \]

3. **Eliminate \(\sqrt{3}\)**:
To simplify, we can divide both sides of the equation by \(\sqrt{3}\):
\[ 36 = \frac{1}{4} a^2 \]

4. **Multiply both sides by 4**:
To isolate \( a^2 \), multiply both sides by 4:
\[ 144 = a^2 \]

5. **Take the square root of both sides**:
Now, take the square root to find \( a \):
\[ a = \sqrt{144} \]

6. **Calculate the square root**:
The square root of 144 is:
\[ a = 12 \text{ cm} \]

Thus, the side of the equilateral triangle is \( 12 \) cm.

### Final Answer:
The side of the equilateral triangle is \( 12 \) cm.