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shubhamsrg

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 ?

  • one year ago
  • one year ago

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

    • one year ago
  2. mukushla
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    im watching :)

    • one year ago
  3. estudier
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    |dw:1350313254678:dw|

    • one year ago
  4. estudier
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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:-(

    • one year ago
  5. estudier
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    Yukky algebra....think, think...

    • one year ago
  6. estudier
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    |dw:1350318976709:dw|

    • one year ago
  7. estudier
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    |dw:1350319309051:dw|

    • one year ago
  8. estudier
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    |dw:1350319508249:dw|

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

    • one year ago
  10. estudier
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    Think that's right...

    • one year ago
  11. shubhamsrg
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    why is 352 half of 362 ?

    • one year ago
  12. estudier
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    Median divides triangle area in half?

    • one year ago
  13. shubhamsrg
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    how is 35 a median ?

    • one year ago
  14. ganeshie8
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    |dw:1350323581495:dw|

    • one year ago
  15. ganeshie8
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    72 || 34 coz 72 is the midsegment

    • one year ago
  16. ganeshie8
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    |dw:1350323706822:dw|

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

    • one year ago
  18. ganeshie8
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    |dw:1350323784808:dw|

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

    • one year ago
  20. ganeshie8
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    it translates to 1672

    • one year ago
  21. shubhamsrg
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    why will 87 meet 6 ?

    • one year ago
  22. ganeshie8
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    diagonals bisect each other in ||gram

    • one year ago
  23. ganeshie8
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    so 65=52

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

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

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

    • one year ago
  27. shubhamsrg
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    i still dont get 876 thing..

    • one year ago
  28. ganeshie8
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    ok did u get estudier diagram

    • one year ago
  29. shubhamsrg
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    yep..i followed every bit till now..

    • one year ago
  30. ganeshie8
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    he constructed, 26 \(\cong\) 47

    • one year ago
  31. shubhamsrg
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    yes..

    • one year ago
  32. ganeshie8
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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)

    • one year ago
  33. shubhamsrg
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    ahh alright,,so 36 isnt a median yet..okay,,

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

    • one year ago
  35. shubhamsrg
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    alright,,

    • one year ago
  36. ganeshie8
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    72 || 84, agree ?

    • one year ago
  37. shubhamsrg
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    yes..

    • one year ago
  38. ganeshie8
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    becoz 72 is the midsegment

    • one year ago
  39. shubhamsrg
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    yes,,i could figure out..

    • one year ago
  40. ganeshie8
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    7284 is a ||gram i have constructed

    • one year ago
  41. shubhamsrg
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    7248*

    • one year ago
  42. shubhamsrg
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    yes,,clear till now..

    • one year ago
  43. ganeshie8
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    also, 74 congruent to 62, by construction

    • one year ago
  44. shubhamsrg
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    okay,,7426 is a //gm..

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

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

    • one year ago
  47. ganeshie8
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    the diagonal in the ||gram 7248 translated to where ?

    • one year ago
  48. shubhamsrg
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    coincides with 62

    • one year ago
  49. ganeshie8
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    |dw:1350324847401:dw|

    • one year ago
  50. ganeshie8
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    the diagonal 74 coincides wid 62 the side 42 coincides wid 21

    • one year ago
  51. shubhamsrg
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    yes,,the 2 //gms are congruent..

    • one year ago
  52. ganeshie8
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    |dw:1350324939445:dw|

    • one year ago
  53. ganeshie8
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    7248 congruent 6127

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

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

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

    • one year ago
  57. ganeshie8
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    whats ur question

    • one year ago
  58. shubhamsrg
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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..

    • one year ago
  59. ganeshie8
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    no

    • one year ago
  60. shubhamsrg
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    ??

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

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

    • one year ago
  63. shubhamsrg
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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)

    • one year ago
  64. ganeshie8
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    ok if that make sense good :)

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

    • one year ago
  66. shubhamsrg
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    yep..

    • one year ago
  67. sauravshakya
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    • one year ago
  68. shubhamsrg
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    excellency yet again..!! thank you @sauravshakya

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

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

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

    • one year ago
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