1. What is the Median of Equilateral Triangle?

The Median of Equilateral Triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. In an equilateral triangle, all medians are equal in length.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( M \) — Median of Equilateral Triangle (m)
• \( r_i \) — Inradius of Equilateral Triangle (m)

3. Formula Explanation

Details: In an equilateral triangle, the median is exactly three times the inradius. This relationship holds true because of the special geometric properties of equilateral triangles where all sides, angles, and special segments maintain consistent ratios.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding median length.

5. Frequently Asked Questions (FAQ)

Q1: Why is the median exactly three times the inradius?
A: This is a fundamental geometric property of equilateral triangles where the distance from the centroid (intersection point of medians) to any vertex is twice the distance to the opposite side, resulting in the 3:1 ratio.

Q2: Does this formula work for all types of triangles?
A: No, this specific relationship only applies to equilateral triangles. Other triangle types have different relationships between medians and inradius.

Q3: What are the units for measurement?
A: The calculator uses meters, but the formula works with any consistent unit system (cm, mm, inches, etc.) as long as both values use the same units.

Q4: Can the inradius be zero?
A: No, the inradius must be a positive value greater than zero for a valid equilateral triangle.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect equilateral triangles. The accuracy depends on the precision of the input value.