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shubhamsrg
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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
 2 years ago
shubhamsrg Group Title
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
 2 years ago

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

mukushla Group TitleBest ResponseYou've already chosen the best response.0
im watching :)
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.0
dw:1350313254678:dw
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.0
x^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:(
 2 years ago

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

estudier Group TitleBest ResponseYou've already chosen the best response.0
dw:1350318976709:dw
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.0
dw:1350319309051:dw
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.0
dw:1350319508249:dw
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.0
152 is a quarter 123 > 123/235 is 4/3 > 143/362 is 4/3 as well
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.0
Think that's right...
 2 years ago

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

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

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

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

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
72  34 coz 72 is the midsegment
 2 years ago

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

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
7824 is a parallelog gram, now imagine we translate it down
 2 years ago

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

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

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

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

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

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
87 meets at 6, thats right, but before that we should prove this : 326 is the triangle made by medians
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
87 meets at 6 becoz, 47 is congruent to 26, 42 is congruent to 21
 2 years ago

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

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

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

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

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

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
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)
 2 years ago

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

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

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
alright,,
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
72  84, agree ?
 2 years ago

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

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

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
7284 is a gram i have constructed
 2 years ago

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

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

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

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

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

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

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
coincides with 62
 2 years ago

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

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

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

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

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
7248 congruent 6127
 2 years ago

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

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

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

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
whats ur question
 2 years ago

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

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

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

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
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)
 2 years ago

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

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

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

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

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

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