A triangle with three equal sides has its area equal to `4.sqrt(3)sq cm`. What will be the perimeter of this triangle?

Answer

To solve the problem step by step, we will find the perimeter of an equilateral triangle given its area.

### Step 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:
\[ A = \frac{\sqrt{3}}{4} a^2 \]

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

### Step 3: Eliminate the square root and solve for \( a^2 \).
To eliminate \( \sqrt{3} \) from both sides, we can divide both sides by \( \sqrt{3} \):
\[ \frac{1}{4} a^2 = 4 \]
Next, multiply both sides by 4 to isolate \( a^2 \):
\[ a^2 = 16 \]

### Step 4: Find the length of the side \( a \).
Now, take the square root of both sides to find \( a \):
\[ a = \sqrt{16} = 4 \text{ cm} \]

### Step 5: Calculate the perimeter of the triangle.
The perimeter \( P \) of an equilateral triangle is given by:
\[ P = 3a \]
Substituting the value of \( a \):
\[ P = 3 \times 4 = 12 \text{ cm} \]

### Conclusion
The perimeter of the triangle is \( 12 \) centimeters.

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