The area of an equilateral triangle is `16sqrt(3)cm^(3)`. Find its side (in cm).
(a)8
(b)4
(c)16
(d)24

Options

A. 8
B. 4
C. 16
D. 24

Answer

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

### Step-by-Step Solution:

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

2. **Substitute the given area into the formula**:
We are given that the area \( A = 16\sqrt{3} \) cm². So we set up the equation:
\[ 16\sqrt{3} = \frac{\sqrt{3}}{4} a^2 \]

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

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

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

6. **Calculate the value of \( a \)**:
\[ a = 8 \text{ cm} \]

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