1. What is the Perimeter of Equilateral Triangle given Inradius?

The perimeter of an equilateral triangle can be calculated from its inradius using the formula P = 6√3 × r_i, where r_i is the inradius. This relationship is derived from the geometric properties of equilateral triangles.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( P \) — Perimeter of Equilateral Triangle (m)
• \( r_i \) — Inradius of Equilateral Triangle (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula establishes a direct proportional relationship between the perimeter and inradius of an equilateral triangle, with the constant factor 6√3.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter from the inradius is useful in various geometric applications, construction projects, and mathematical problems involving equilateral triangles.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive (inradius > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is an inradius?
A: The inradius is the radius of the largest circle that fits inside the triangle, tangent to all three sides.

Q2: Why is there a √3 in the formula?
A: The √3 factor comes from the trigonometric relationships in an equilateral triangle, specifically from the 60-degree angles.

Q3: Can this formula be used for other types of triangles?
A: No, this specific formula only applies to equilateral triangles. Other triangle types have different relationships between perimeter and inradius.

Q4: What are the units for the result?
A: The result will be in the same units as the input. If you enter inradius in meters, the perimeter will be in meters.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input values and using the exact value of √3.