The perimeter of an equilateral triangle whose area is `4sqrt3 cm^(2) ` is equal to
(a) 10 cm
(b) 12 cm
(c) 15 cm
(d) 20 cm

Options

A. 10 cm
B. 12 cm
C. 15 cm
D. 20 cm

Answer

To find the perimeter of an equilateral triangle whose area is given as \(4\sqrt{3} \, \text{cm}^2\), we can follow these steps:

### Step 1: Use the formula for the area of an equilateral triangle
The area \(A\) of an equilateral triangle with side length \(a\) is given by the formula:
\[ A = \frac{\sqrt{3}}{4} a^2 \]
Given that the area is \(4\sqrt{3} \, \text{cm}^2\), we can set up the equation:
\[ \frac{\sqrt{3}}{4} a^2 = 4\sqrt{3} \]

### Step 2: Solve for \(a^2\)
To isolate \(a^2\), we can multiply both sides by 4:
\[ \sqrt{3} a^2 = 16\sqrt{3} \]
Next, divide both sides by \(\sqrt{3}\):
\[ a^2 = 16 \]

### Step 3: Find the side length \(a\)
Taking the square root of both sides, we find:
\[ a = 4 \, \text{cm} \]

### Step 4: Calculate the perimeter
The perimeter \(P\) of an equilateral triangle is given by:
\[ P = 3a \]
Substituting the value of \(a\):
\[ P = 3 \times 4 = 12 \, \text{cm} \]

### Final Answer
Thus, the perimeter of the equilateral triangle is \(12 \, \text{cm}\).