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April 19, 2015

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)

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