Understanding the Area of an Equilateral Triangle
The area (A) of an equilateral triangle can be calculated using the formula:
A = (sqrt(3)/4) * s^2
where "s" is the length of a side of the triangle.
Given Information
- The area of the equilateral triangle is 16√3 cm².
Setting Up the Equation
1. Substitute the area into the formula:
- 16√3 = (sqrt(3)/4) * s^2
2. To eliminate the fraction, multiply both sides by 4:
- 4 * 16√3 = sqrt(3) * s^2
- 64√3 = sqrt(3) * s^2
Isolating s²
3. Divide both sides by sqrt(3):
- s^2 = 64√3 / sqrt(3)
- s^2 = 64
Finding the Side Length
4. Take the square root of both sides to find "s":
- s = sqrt(64)
- s = 8 cm
Conclusion
- The side length of the equilateral triangle is 8 cm.
This step-by-step breakdown simplifies the process of finding the side length from the given area. Understanding the derivation of the formula and manipulating it correctly leads to the correct side length. Always remember to check your calculations for accuracy!