Edge Length of Equilateral Triangle given Inradius Calculator

Formula Used:

\[ Edge\ Length\ of\ Equilateral\ Triangle = 2 \times \sqrt{3} \times Inradius\ of\ Equilateral\ Triangle \] \[ l_e = 2 \times \sqrt{3} \times r_i \]

Edge Length of Equilateral Triangle:

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1. What is the Edge Length of Equilateral Triangle given Inradius Formula?

The formula calculates the edge length of an equilateral triangle from its inradius. In an equilateral triangle, all three sides are equal and all three angles are 60 degrees. The inradius is the radius of the inscribed circle that touches all three sides.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Edge\ Length\ of\ Equilateral\ Triangle = 2 \times \sqrt{3} \times Inradius\ of\ Equilateral\ Triangle \] \[ l_e = 2 \times \sqrt{3} \times r_i \]

Where:

\( l_e \) — Edge Length of Equilateral Triangle (meters)
\( r_i \) — Inradius of Equilateral Triangle (meters)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula derives from the geometric relationship between the side length and inradius in an equilateral triangle, where the inradius is exactly \( \frac{\sqrt{3}}{6} \) times the side length.

3. Importance of Edge Length Calculation

Details: Calculating the edge length from the inradius is important in geometry, architecture, and engineering applications where equilateral triangles are used. It helps in determining the size and proportions of triangular structures and components.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive (inradius > 0). The calculator will compute the corresponding edge length of the equilateral triangle.

5. Frequently Asked Questions (FAQ)

Q1: What is an equilateral triangle?
A: An equilateral triangle is a triangle with all three sides of equal length and all three angles equal to 60 degrees.

Q2: What is the inradius of a triangle?
A: The inradius is the radius of the inscribed circle (incircle) that touches all three sides of the triangle.

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

Q4: What is the relationship between inradius and circumradius in an equilateral triangle?
A: In an equilateral triangle, the circumradius is exactly twice the inradius (\( R = 2r \)).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, provided the input values are accurate and the triangle is perfectly equilateral.