The area of an equilateral triangle is `4sqrt3 cm^(2)`. The length of each of its sides is

Options

A. 3cm
B. 4cm
C. `2sqrt3m`
D. `(1)/(2)sqrt3cm`

Answer

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:

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

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

### Step-by-Step Solution:

1. **Write down the area formula:**
\[ \text{Area} = \frac{\sqrt{3}}{4} s^2 \]

2. **Substitute the given area into the formula:**
We know that the area is \( 4\sqrt{3} \, \text{cm}^2 \).
\[ 4\sqrt{3} = \frac{\sqrt{3}}{4} s^2 \]

3. **Multiply both sides by 4 to eliminate the fraction:**
\[ 4 \times 4\sqrt{3} = \sqrt{3} s^2 \]
\[ 16\sqrt{3} = \sqrt{3} s^2 \]

4. **Divide both sides by \(\sqrt{3}\):**
\[ \frac{16\sqrt{3}}{\sqrt{3}} = s^2 \]
\[ 16 = s^2 \]

5. **Take the square root of both sides to find \( s \):**
\[ s = \sqrt{16} \]
\[ s = 4 \, \text{cm} \]

### Final Answer:
The length of each side of the equilateral triangle is \( 4 \, \text{cm} \).