The area of an equilateral triangle is `(16 xx sqrt3) cm^(2)`. Find 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-by-Step Solution:

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

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

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

4. **Multiply both sides by 4**:
To isolate \( s^2 \), multiply both sides of the equation by 4:
\[ 64 = s^2 \]

5. **Take the square root of both sides**:
To find \( s \), take the square root of both sides:
\[ s = \sqrt{64} \]

6. **Calculate the square root**:
The square root of 64 is:
\[ s = 8 \text{ cm} \]

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

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