If the length of each side of an equilateral triangle of area `4sqrt(3)\ c m^2,\ ` is

Options

A. `4 c m`
B. `4/(sqrt(3))c m `
C. `(sqrt(3))/4 c m`
D. `3 c m`

Answer

To find the length of each side of an equilateral triangle given its area, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Area Formula**:
The area \( A \) of an equilateral triangle with side length \( a \) is given by the formula:
\[ A = \frac{\sqrt{3}}{4} a^2 \]

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

3. **Eliminate the Fraction**:
To eliminate the fraction, we can multiply both sides of the equation by 4:
\[ 4 \times 4\sqrt{3} = \sqrt{3} a^2 \]
This simplifies to:
\[ 16\sqrt{3} = \sqrt{3} a^2 \]

4. **Divide by \(\sqrt{3}\)**:
Next, we divide both sides by \(\sqrt{3}\) (assuming \(\sqrt{3} \neq 0\)):
\[ \frac{16\sqrt{3}}{\sqrt{3}} = a^2 \]
This simplifies to:
\[ 16 = a^2 \]

5. **Take the Square Root**:
To find \( a \), we take the square root of both sides:
\[ a = \sqrt{16} \]
Thus, we find:
\[ a = 4 \, \text{cm} \]

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

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