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shubhamsrg

  • 3 years ago

what is the ratio of area of a traingle ABC to the area of the triangle whose sides are equal to the medians of ABC ?

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  1. shubhamsrg
    • 3 years ago
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    or,,prove that this ratio always equals 4/3

  2. mukushla
    • 3 years ago
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    im watching :)

  3. estudier
    • 3 years ago
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    |dw:1350313254678:dw|

  4. estudier
    • 3 years ago
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    x^2 + h^2 = c^2 and y^2 +h^2 = b^2, x+y = a x^2-y^2 = c^2-b^2 ......hmm might be better off with Cosine Rule:-(

  5. estudier
    • 3 years ago
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    Yukky algebra....think, think...

  6. estudier
    • 3 years ago
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    |dw:1350318976709:dw|

  7. estudier
    • 3 years ago
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    |dw:1350319309051:dw|

  8. estudier
    • 3 years ago
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    |dw:1350319508249:dw|

  9. estudier
    • 3 years ago
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    152 is a quarter 123 -> 123/235 is 4/3 -> 143/362 is 4/3 as well

  10. estudier
    • 3 years ago
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    Think that's right...

  11. shubhamsrg
    • 3 years ago
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    why is 352 half of 362 ?

  12. estudier
    • 3 years ago
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    Median divides triangle area in half?

  13. shubhamsrg
    • 3 years ago
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    how is 35 a median ?

  14. ganeshie8
    • 3 years ago
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    |dw:1350323581495:dw|

  15. ganeshie8
    • 3 years ago
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    72 || 34 coz 72 is the midsegment

  16. ganeshie8
    • 3 years ago
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    |dw:1350323706822:dw|

  17. ganeshie8
    • 3 years ago
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    7824 is a parallelog gram, now imagine we translate it down

  18. ganeshie8
    • 3 years ago
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    |dw:1350323784808:dw|

  19. estudier
    • 3 years ago
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    Yes, sorry, I didn't make the construction very clear.......

  20. ganeshie8
    • 3 years ago
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    it translates to 1672

  21. shubhamsrg
    • 3 years ago
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    why will 87 meet 6 ?

  22. ganeshie8
    • 3 years ago
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    diagonals bisect each other in ||gram

  23. ganeshie8
    • 3 years ago
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    so 65=52

  24. ganeshie8
    • 3 years ago
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    87 meets at 6, thats right, but before that we should prove this : 326 is the triangle made by medians

  25. ganeshie8
    • 3 years ago
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    87 meets at 6 becoz, 47 is congruent to 26, 42 is congruent to 21

  26. ganeshie8
    • 3 years ago
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    the only tricky part in this proof i see is proving this : 326 is the triangle made by medians

  27. shubhamsrg
    • 3 years ago
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    i still dont get 876 thing..

  28. ganeshie8
    • 3 years ago
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    ok did u get estudier diagram

  29. shubhamsrg
    • 3 years ago
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    yep..i followed every bit till now..

  30. ganeshie8
    • 3 years ago
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    he constructed, 26 \(\cong\) 47

  31. shubhamsrg
    • 3 years ago
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    yes..

  32. ganeshie8
    • 3 years ago
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    26 is just translation of 47, so they are || one more construction he did is, he translated other median also, the translated medians intersect at 6. (we can prove this, later)

  33. shubhamsrg
    • 3 years ago
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    ahh alright,,so 36 isnt a median yet..okay,,

  34. ganeshie8
    • 3 years ago
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    assume it is a median so that we prove the thing at hand, :)

  35. shubhamsrg
    • 3 years ago
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    alright,,

  36. ganeshie8
    • 3 years ago
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    72 || 84, agree ?

  37. shubhamsrg
    • 3 years ago
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    yes..

  38. ganeshie8
    • 3 years ago
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    becoz 72 is the midsegment

  39. shubhamsrg
    • 3 years ago
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    yes,,i could figure out..

  40. ganeshie8
    • 3 years ago
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    7284 is a ||gram i have constructed

  41. shubhamsrg
    • 3 years ago
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    7248*

  42. shubhamsrg
    • 3 years ago
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    yes,,clear till now..

  43. ganeshie8
    • 3 years ago
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    also, 74 congruent to 62, by construction

  44. shubhamsrg
    • 3 years ago
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    okay,,7426 is a //gm..

  45. ganeshie8
    • 3 years ago
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    now imagine we slide the ||gram 7248 along the side 41

  46. shubhamsrg
    • 3 years ago
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    so you're saying those 2 //gms are congruent..

  47. ganeshie8
    • 3 years ago
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    the diagonal in the ||gram 7248 translated to where ?

  48. shubhamsrg
    • 3 years ago
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    coincides with 62

  49. ganeshie8
    • 3 years ago
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    |dw:1350324847401:dw|

  50. ganeshie8
    • 3 years ago
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    the diagonal 74 coincides wid 62 the side 42 coincides wid 21

  51. shubhamsrg
    • 3 years ago
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    yes,,the 2 //gms are congruent..

  52. ganeshie8
    • 3 years ago
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    |dw:1350324939445:dw|

  53. ganeshie8
    • 3 years ago
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    7248 congruent 6127

  54. ganeshie8
    • 3 years ago
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    we just use this : 6127 is a ||gram that gives 5 is midpoint of diagonal 62

  55. shubhamsrg
    • 3 years ago
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    that one we already knew right ?

  56. ganeshie8
    • 3 years ago
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    which one ? i thought we're trying to prove 5 is midpoint of 62 lol

  57. ganeshie8
    • 3 years ago
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    whats ur question

  58. shubhamsrg
    • 3 years ago
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    we knew 5 was the mid point quite earlier..after that assumption, everything fitted..those 2 became congruent //gms and everything else..

  59. ganeshie8
    • 3 years ago
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    no

  60. shubhamsrg
    • 3 years ago
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    ??

  61. ganeshie8
    • 3 years ago
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    those 2 became congruent || grams by construction, 5 got nothing to do wid it

  62. ganeshie8
    • 3 years ago
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    let me put everything in one reply

  63. shubhamsrg
    • 3 years ago
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    we assumed 36 to be the median..that gave 16 // 27 ..by which it was a //gm,, and thus 5 was the midpoint ( 2 diagnols intersected)

  64. ganeshie8
    • 3 years ago
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    ok if that make sense good :)

  65. ganeshie8
    • 3 years ago
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    so only assumption we need to prove is 36 is a median, right ?

  66. shubhamsrg
    • 3 years ago
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    yep..

  67. sauravshakya
    • 3 years ago
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  68. shubhamsrg
    • 3 years ago
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    excellency yet again..!! thank you @sauravshakya

  69. shubhamsrg
    • 3 years ago
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    and big thank you to @ganeshie8 ..your idea was used here after all..

  70. shubhamsrg
    • 3 years ago
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    + @estudier you sparked the figure, ofcourse ! :P

  71. estudier
    • 3 years ago
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    I managed to get an outline of this just with algebra --- what a mess!!

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