The area of an equilateral triangle is `36sqrt(3)` sq. cm. Find its perimeter.

Answer

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 \( a \) is given by the formula:
\[ A = \frac{\sqrt{3}}{4} a^2 \]

### Step 2: Substitute the given area into the formula.
We know the area is \( 36\sqrt{3} \) sq. cm. So we can set up the equation:
\[ 36\sqrt{3} = \frac{\sqrt{3}}{4} a^2 \]

### Step 3: Eliminate \( \sqrt{3} \) from both sides.
To simplify the equation, we can divide both sides by \( \sqrt{3} \):
\[ 36 = \frac{1}{4} a^2 \]

### Step 4: Multiply both sides by 4 to solve for \( a^2 \).
\[ 36 \times 4 = a^2 \]
\[ 144 = a^2 \]

### Step 5: Take the square root of both sides to find \( a \).
\[ a = \sqrt{144} \]
\[ a = 12 \text{ cm} \]

### Step 6: Calculate the perimeter of the equilateral triangle.
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 \( 36 \) cm.

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