Friday

October 24, 2014

October 24, 2014

Posted by **POD** on Sunday, March 23, 2008 at 11:53am.

3(A^2+B^2+C^2)=4(a^2+b^2+c^2)

(sides) = (medians)

- math -
**Qun**, Monday, March 24, 2008 at 1:59amThe standard notation for the length of medians:

a=(1/2)*sqrt(2C^2+2B^2-A^2)

b=(1/2)*sqrt(2C^2+2A^2-B^2)

c=(1/2)*sqrt(2A^2+2B^2-C^2)

square both sides:

a^2=(1/4)*(2C^2+2B^2-A^2)

b^2=(1/4)*(2C^2+2A^2-B^2)

c^2=(1/4)*(2A^2+2B^2-C^2)

multiply 4 on both sides:

4a^2=(2C^2+2B^2-A^2)

4b^2=(2C^2+2A^2-B^2)

4c^2=(2A^2+2B^2-C^2)

add them all vertically:

you get:

4(a^2+b^2+c^2)=3(A^2+B^2+C^2)

**Answer this Question**

**Related Questions**

Math - A triangle has vertices X(0,0), Y(4,4), and Z (8,-4). a) Write an ...

Geometry - How do you find the lengths of the sides of an isosceles triangle ...

geometry - If two medians of a triangle are equal, prove that the triangle ...

Math - 12. In a triangle ABC, AC = 36, BC = 48, and the medians BD and AE to ...

geometry - Write a two column proof. Given CE = CA, EB and AD are medians, Prove...

Geometry - Given a triangle ABC with A(6b,6c) B(0,0) and C (6a,0), prove that ...

geometry question proof needed - Medians AX and BY of Triangle ABC are ...

Math - In a triangle ABC, AC = 36, BC = 48, and the medians BD and AE to sides ...

Geometry: Ms. Sue or Steve or someone help please? - Given a triangle ABC with A...

geometry - show that the sum of the squares of the lengths of the medians of ...