If the numerical value of the perimeter of an equilateral triangle is `sqrt(3)`  times the area of it, then the length of each side of the triangle is

Options

A. 2 units
B. 3 units
C. 4 units
D. 6 units

Answer

To solve the problem, we need to find the length of each side of an equilateral triangle given that the numerical value of its perimeter is equal to \(\sqrt{3}\) times its area.

### Step-by-Step Solution:

1. **Define the Side Length**:
Let the length of each side of the equilateral triangle be \(a\).

2. **Calculate the Perimeter**:
The perimeter \(P\) of an equilateral triangle is given by:
\[ P = 3a \]

3. **Calculate the Area**:
The area \(A\) of an equilateral triangle can be calculated using the formula:
\[ A = \frac{\sqrt{3}}{4} a^2 \]

4. **Set Up the Equation**:
According to the problem, the perimeter is equal to \(\sqrt{3}\) times the area:
\[ 3a = \sqrt{3} \cdot A \]
Substituting the expression for the area \(A\):
\[ 3a = \sqrt{3} \cdot \left(\frac{\sqrt{3}}{4} a^2\right) \]

5. **Simplify the Equation**:
This simplifies to:
\[ 3a = \frac{3}{4} a^2 \]

6. **Rearranging the Equation**:
Multiply both sides by 4 to eliminate the fraction:
\[ 12a = 3a^2 \]
Rearranging gives:
\[ 3a^2 - 12a = 0 \]

7. **Factor the Equation**:
Factor out \(3a\):
\[ 3a(a - 4) = 0 \]

8. **Solve for \(a\)**:
Setting each factor to zero gives:
\[ 3a = 0 \quad \text{or} \quad a - 4 = 0 \]
Thus, \(a = 0\) (not valid for a triangle) or:
\[ a = 4 \]

### Conclusion:
The length of each side of the triangle is \(4\) units.