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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 ?
 one year ago
 one year 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 ?
 one year ago
 one year ago

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shubhamsrgBest ResponseYou've already chosen the best response.0
or,,prove that this ratio always equals 4/3
 one year ago

estudierBest ResponseYou've already chosen the best response.0
dw:1350313254678:dw
 one year ago

estudierBest 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:(
 one year ago

estudierBest ResponseYou've already chosen the best response.0
Yukky algebra....think, think...
 one year ago

estudierBest ResponseYou've already chosen the best response.0
dw:1350318976709:dw
 one year ago

estudierBest ResponseYou've already chosen the best response.0
dw:1350319309051:dw
 one year ago

estudierBest ResponseYou've already chosen the best response.0
dw:1350319508249:dw
 one year ago

estudierBest 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
 one year ago

estudierBest ResponseYou've already chosen the best response.0
Think that's right...
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
why is 352 half of 362 ?
 one year ago

estudierBest ResponseYou've already chosen the best response.0
Median divides triangle area in half?
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
how is 35 a median ?
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
dw:1350323581495:dw
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
72  34 coz 72 is the midsegment
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
dw:1350323706822:dw
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
7824 is a parallelog gram, now imagine we translate it down
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
dw:1350323784808:dw
 one year ago

estudierBest ResponseYou've already chosen the best response.0
Yes, sorry, I didn't make the construction very clear.......
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
it translates to 1672
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
why will 87 meet 6 ?
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
diagonals bisect each other in gram
 one year ago

ganeshie8Best 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
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
87 meets at 6 becoz, 47 is congruent to 26, 42 is congruent to 21
 one year ago

ganeshie8Best 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
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
i still dont get 876 thing..
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
ok did u get estudier diagram
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
yep..i followed every bit till now..
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
he constructed, 26 \(\cong\) 47
 one year ago

ganeshie8Best 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)
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
ahh alright,,so 36 isnt a median yet..okay,,
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
assume it is a median so that we prove the thing at hand, :)
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
becoz 72 is the midsegment
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
yes,,i could figure out..
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
7284 is a gram i have constructed
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
yes,,clear till now..
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
also, 74 congruent to 62, by construction
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
okay,,7426 is a //gm..
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
now imagine we slide the gram 7248 along the side 41
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
so you're saying those 2 //gms are congruent..
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
the diagonal in the gram 7248 translated to where ?
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
dw:1350324847401:dw
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
the diagonal 74 coincides wid 62 the side 42 coincides wid 21
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
yes,,the 2 //gms are congruent..
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
dw:1350324939445:dw
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
we just use this : 6127 is a gram that gives 5 is midpoint of diagonal 62
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
that one we already knew right ?
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
which one ? i thought we're trying to prove 5 is midpoint of 62 lol
 one year ago

shubhamsrgBest 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..
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
those 2 became congruent  grams by construction, 5 got nothing to do wid it
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
let me put everything in one reply
 one year ago

shubhamsrgBest 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)
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
ok if that make sense good :)
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
so only assumption we need to prove is 36 is a median, right ?
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
excellency yet again..!! thank you @sauravshakya
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
and big thank you to @ganeshie8 ..your idea was used here after all..
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
+ @estudier you sparked the figure, ofcourse ! :P
 one year ago

estudierBest ResponseYou've already chosen the best response.0
I managed to get an outline of this just with algebra  what a mess!!
 one year ago
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