## anonymous 4 years ago Challenge: Find the ratio of area of triangle and area of triangle formed using the lengths of the medians.

1. anonymous

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

2. Directrix

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

3. anonymous

No

4. anonymous

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

5. anonymous

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

6. anonymous

That is right aron

7. anonymous

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

8. anonymous

Yep it's 3/4.

9. anonymous

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

10. anonymous

I know a proof using vectors

11. anonymous

Aha, vector would certainly make things much easy.

12. anonymous

It is a 3 line proof And i discovered it myself

13. anonymous

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 .

14. anonymous

@Aron that's a fairly complicated form.