Median on Medium Side of Scalene Triangle given Three Sides Calculator

Formula Used:

\[ M_{Medium} = \frac{\sqrt{2 \times (S_{Longer}^2 + S_{Shorter}^2) - S_{Medium}^2}}{2} \]

Longer Side of Scalene Triangle:

Shorter Side of Scalene Triangle:

Medium Side of Scalene Triangle:

Median on Medium Side of Scalene Triangle:

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1. What is Median on Medium Side of Scalene Triangle?

The Median on Medium Side of Scalene Triangle is a line segment joining the midpoint of the medium side to its opposite vertex. In a scalene triangle, all three sides have different lengths, and the median divides the medium side into two equal parts.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M_{Medium} = \frac{\sqrt{2 \times (S_{Longer}^2 + S_{Shorter}^2) - S_{Medium}^2}}{2} \]

Where:

\( M_{Medium} \) — Median on Medium Side of Scalene Triangle (m)
\( S_{Longer} \) — Longer Side of Scalene Triangle (m)
\( S_{Shorter} \) — Shorter Side of Scalene Triangle (m)
\( S_{Medium} \) — Medium Side of Scalene Triangle (m)

Explanation: This formula calculates the length of the median drawn to the medium side of a scalene triangle using the lengths of all three sides.

3. Importance of Median Calculation

Details: Medians are important geometric elements in triangles. They help in finding the centroid (center of mass) of the triangle and are used in various geometric proofs and constructions.

4. Using the Calculator

Tips: Enter the lengths of all three sides of the scalene triangle in meters. Make sure the values are positive and follow the triangle inequality theorem.

5. Frequently Asked Questions (FAQ)

Q1: What is a scalene triangle?
A: A scalene triangle is a triangle in which all three sides have different lengths, and consequently all three angles are different.

Q2: How many medians does a triangle have?
A: Every triangle has three medians, one from each vertex to the midpoint of the opposite side.

Q3: Do all medians in a scalene triangle have different lengths?
A: Yes, in a scalene triangle, all three medians have different lengths since all sides are unequal.

Q4: What is the relationship between medians and the centroid?
A: The three medians of a triangle intersect at a single point called the centroid, which divides each median in a 2:1 ratio.

Q5: Can this formula be used for other types of triangles?
A: Yes, this formula works for any triangle, but it's specifically mentioned for scalene triangles since in equilateral or isosceles triangles, some medians may have equal lengths.