The area of an equilateral triangle is `36 sqrt(3) cm^(2)`. Its perimeter is

Options

A. 36 cm
B. `12 sqrt(3)` cm
C. 24 cm
D. 30 cm

Answer

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

### Step-by-Step Solution:

1. **Understand 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:
\[ A = \frac{\sqrt{3}}{4} a^2 \]

2. **Set the area equal to the given value**:
We know the area of the triangle is \( 36\sqrt{3} \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ \frac{\sqrt{3}}{4} a^2 = 36\sqrt{3} \]

3. **Eliminate \(\sqrt{3}\) from both sides**:
We can divide both sides of the equation by \(\sqrt{3}\):
\[ \frac{1}{4} a^2 = 36 \]

4. **Multiply both sides by 4**:
To isolate \( a^2 \), multiply both sides by 4:
\[ a^2 = 36 \times 4 \]
\[ a^2 = 144 \]

5. **Take the square root of both sides**:
To find \( a \), take the square root:
\[ a = \sqrt{144} \]
\[ a = 12 \, \text{cm} \]

6. **Calculate the perimeter**:
The perimeter \( P \) of an equilateral triangle is given by:
\[ P = 3a \]
Substituting the value of \( a \):
\[ P = 3 \times 12 = 36 \, \text{cm} \]

### Final Answer:
The perimeter of the equilateral triangle is \( 36 \, \text{cm} \).

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