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 and intersect at the centroid.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula calculates the median length based on the perimeter of an equilateral triangle, utilizing the mathematical relationship between the side length and median in such triangles.

3. Importance of Median Calculation

Details: Calculating the median is important in geometry for determining various properties of equilateral triangles, including centroid location, area division, and symmetry analysis.

4. Using the Calculator

Tips: Enter the perimeter of the equilateral triangle in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: Are all medians equal in an equilateral triangle?
A: Yes, in an equilateral triangle, all three medians are equal in length due to the symmetry of the triangle.

Q2: How is the median related to the side length?
A: In an equilateral triangle, the median is equal to \( \frac{\sqrt{3}}{2} \) times the side length.

Q3: What is the relationship between median and altitude?
A: In an equilateral triangle, the median, altitude, and angle bisector are all the same line segment.

Q4: 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 median calculations.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect equilateral triangles, assuming precise input values.