The area of an equilateral triangle is `16sqrt(3)cm^(2)` then what will be the length of each side of the triangle?

Answer

To find the length of each side 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 from the problem that the area \( A \) is \( 16\sqrt{3} \, \text{cm}^2 \). So we can set up the equation:
\[ 16\sqrt{3} = \frac{\sqrt{3}}{4} a^2 \]

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

### Step 4: Multiply both sides by 4 to isolate \( a^2 \).
\[ 16 \times 4 = a^2 \]
\[ 64 = a^2 \]

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

### Final Answer:
The length of each side of the equilateral triangle is \( 8 \, \text{cm} \).

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