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anonymous

  • 4 years ago

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

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  1. anonymous
    • 4 years ago
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    Sorry it is not a challenge it took me 2mins to realize the solution

  2. Directrix
    • 4 years ago
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    If we're talking a single triangle, the area would be constant and the ratio 1:1.

  3. anonymous
    • 4 years ago
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    No

  4. anonymous
    • 4 years ago
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    area of the triangle of medians is three-fourths of the area of the given triangle.

  5. anonymous
    • 4 years ago
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    three medians of a triangle divide the triangle into six equal areas.

  6. anonymous
    • 4 years ago
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    That is right aron

  7. anonymous
    • 4 years ago
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    However tell me how did you do it just want to check if we both used the same method

  8. anonymous
    • 4 years ago
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    Yep it's 3/4.

  9. anonymous
    • 4 years ago
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    I used this: http://mathworld.wolfram.com/TriangleMedian.html

  10. anonymous
    • 4 years ago
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    I know a proof using vectors

  11. anonymous
    • 4 years ago
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    Aha, vector would certainly make things much easy.

  12. anonymous
    • 4 years ago
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    It is a 3 line proof And i discovered it myself

  13. anonymous
    • 4 years ago
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    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
    • 4 years ago
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    @Aron that's a fairly complicated form.

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