Triangle Median Length

\[m_c=\frac{1}{2}\sqrt{2a^2+2b^2-c^2}\]

mC = median length to side c (m)

a = triangle side a (m)

b = triangle side b (m)

c = triangle side c (m)

This geometric formula calculates the length of a triangle median using the lengths of the three sides.

A median is a line segment drawn from a vertex to the midpoint of the opposite side.

The formula is derived from Apollonius' theorem and works for any triangle.

Use this formula when:

- The three side lengths of the triangle are known

- The median length must be calculated

- Solving geometry or structural problems

- Working with triangle subdivisions

- Analyzing geometric properties of triangles

This formula applies to scalene, isosceles, and equilateral triangles.

If:

a = 8 m

b = 10 m

c = 12 m

Then:

mC = (1/2)*√(2*8²+2*10²-12²)

mC = (1/2)*√(128+200-144)

mC = (1/2)*√184

mC ≈ 6.78 m

- Geometry and trigonometry

- Structural engineering

- Architecture and design

- CAD and 3D modeling

- Physics calculations

- Educational mathematics

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