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 2 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 ?
 2 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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shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0or,,prove that this ratio always equals 4/3

estudier
 2 years ago
Best ResponseYou've already chosen the best response.0x^2 + h^2 = c^2 and y^2 +h^2 = b^2, x+y = a x^2y^2 = c^2b^2 ......hmm might be better off with Cosine Rule:(

estudier
 2 years ago
Best ResponseYou've already chosen the best response.0Yukky algebra....think, think...

estudier
 2 years ago
Best ResponseYou've already chosen the best response.0152 is a quarter 123 > 123/235 is 4/3 > 143/362 is 4/3 as well

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0why is 352 half of 362 ?

estudier
 2 years ago
Best ResponseYou've already chosen the best response.0Median divides triangle area in half?

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0how is 35 a median ?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1350323581495:dw

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.072  34 coz 72 is the midsegment

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1350323706822:dw

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.07824 is a parallelog gram, now imagine we translate it down

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1350323784808:dw

estudier
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, sorry, I didn't make the construction very clear.......

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0it translates to 1672

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0why will 87 meet 6 ?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0diagonals bisect each other in gram

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.087 meets at 6, thats right, but before that we should prove this : 326 is the triangle made by medians

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.087 meets at 6 becoz, 47 is congruent to 26, 42 is congruent to 21

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0the only tricky part in this proof i see is proving this : 326 is the triangle made by medians

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0i still dont get 876 thing..

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0ok did u get estudier diagram

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0yep..i followed every bit till now..

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0he constructed, 26 \(\cong\) 47

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.026 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)

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0ahh alright,,so 36 isnt a median yet..okay,,

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0assume it is a median so that we prove the thing at hand, :)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0becoz 72 is the midsegment

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0yes,,i could figure out..

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.07284 is a gram i have constructed

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0yes,,clear till now..

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0also, 74 congruent to 62, by construction

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0okay,,7426 is a //gm..

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0now imagine we slide the gram 7248 along the side 41

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0so you're saying those 2 //gms are congruent..

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0the diagonal in the gram 7248 translated to where ?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1350324847401:dw

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0the diagonal 74 coincides wid 62 the side 42 coincides wid 21

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0yes,,the 2 //gms are congruent..

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1350324939445:dw

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0we just use this : 6127 is a gram that gives 5 is midpoint of diagonal 62

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0that one we already knew right ?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0which one ? i thought we're trying to prove 5 is midpoint of 62 lol

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0we knew 5 was the mid point quite earlier..after that assumption, everything fitted..those 2 became congruent //gms and everything else..

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0those 2 became congruent  grams by construction, 5 got nothing to do wid it

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0let me put everything in one reply

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0we 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)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0ok if that make sense good :)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.0so only assumption we need to prove is 36 is a median, right ?

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0excellency yet again..!! thank you @sauravshakya

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0and big thank you to @ganeshie8 ..your idea was used here after all..

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0+ @estudier you sparked the figure, ofcourse ! :P

estudier
 2 years ago
Best ResponseYou've already chosen the best response.0I managed to get an outline of this just with algebra  what a mess!!
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