Question

Challenge:
Find the ratio of area of triangle and area of triangle formed using the lengths of the medians.

Answer 1

Sorry it is not a challenge it took me 2mins to realize the solution

Answer 2

If we're talking a single triangle, the area would be constant and the ratio 1:1.

Answer 3

No

Answer 4

area of the triangle of medians is three-fourths of the area of the given triangle.

Answer 5

three medians of a triangle divide the triangle into six equal areas.

Answer 6

That is right aron

Answer 7

However tell me how did you do it just want to check if we both used the same method

Answer 8

Yep it's 3/4.

Answer 9

I used this: http://mathworld.wolfram.com/TriangleMedian.html

Answer 10

I know a proof using vectors

Answer 11

Aha, vector would certainly make things much easy.

Answer 12

It is a 3 line proof
And i discovered it myself

Answer 13

Furthermore, the area of the triangle is :
\[1/3\sqrt{(2\sum u ^{2}v ^{2} - \sum u^{4})}\]
where u,v and w are the medians .

Answer 14

@Aron that's a fairly complicated form.