If the area of an equilateral triangle is `16sqrt3 cm^(2)`, then the perimeter of the triangle is

Options

A. 48 cm
B. 24 cm
C. 12 cm
D. 36 cm

Explanation

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

### Step 1: Write down the formula for the area of an equilateral triangle.
The area \( A \) of an equilateral triangle with side length \( x \) is given by the formula:
\[ A = \frac{\sqrt{3}}{4} x^2 \]

### Step 2: Set the area equal to the given value.
We know from the problem that the area is \( 16\sqrt{3} \) cm². Therefore, we can set up the equation:
\[ \frac{\sqrt{3}}{4} x^2 = 16\sqrt{3} \]

### Step 3: Eliminate \( \sqrt{3} \) from both sides.
To simplify the equation, we can divide both sides by \( \sqrt{3} \):
\[ \frac{1}{4} x^2 = 16 \]

### Step 4: Multiply both sides by 4.
To isolate \( x^2 \), multiply both sides by 4:
\[ x^2 = 16 \times 4 \]
\[ x^2 = 64 \]

### Step 5: Take the square root of both sides.
Now, take the square root to find \( x \):
\[ x = \sqrt{64} \]
\[ x = 8 \text{ cm} \]

### Step 6: Calculate the perimeter of the equilateral triangle.
The perimeter \( P \) of an equilateral triangle is given by:
\[ P = 3 \times \text{side} \]
Substituting the value of the side:
\[ P = 3 \times 8 = 24 \text{ cm} \]

### Final Answer:
The perimeter of the triangle is \( 24 \text{ cm} \).

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