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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 ?

Mathematics
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or,,prove that this ratio always equals 4/3
im watching :)
|dw:1350313254678:dw|

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Other answers:

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:-(
Yukky algebra....think, think...
|dw:1350318976709:dw|
|dw:1350319309051:dw|
|dw:1350319508249:dw|
152 is a quarter 123 -> 123/235 is 4/3 -> 143/362 is 4/3 as well
Think that's right...
why is 352 half of 362 ?
Median divides triangle area in half?
how is 35 a median ?
|dw:1350323581495:dw|
72 || 34 coz 72 is the midsegment
|dw:1350323706822:dw|
7824 is a parallelog gram, now imagine we translate it down
|dw:1350323784808:dw|
Yes, sorry, I didn't make the construction very clear.......
it translates to 1672
why will 87 meet 6 ?
diagonals bisect each other in ||gram
so 65=52
87 meets at 6, thats right, but before that we should prove this : 326 is the triangle made by medians
87 meets at 6 becoz, 47 is congruent to 26, 42 is congruent to 21
the only tricky part in this proof i see is proving this : 326 is the triangle made by medians
i still dont get 876 thing..
ok did u get estudier diagram
yep..i followed every bit till now..
he constructed, 26 \(\cong\) 47
yes..
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)
ahh alright,,so 36 isnt a median yet..okay,,
assume it is a median so that we prove the thing at hand, :)
alright,,
72 || 84, agree ?
yes..
becoz 72 is the midsegment
yes,,i could figure out..
7284 is a ||gram i have constructed
7248*
yes,,clear till now..
also, 74 congruent to 62, by construction
okay,,7426 is a //gm..
now imagine we slide the ||gram 7248 along the side 41
so you're saying those 2 //gms are congruent..
the diagonal in the ||gram 7248 translated to where ?
coincides with 62
|dw:1350324847401:dw|
the diagonal 74 coincides wid 62 the side 42 coincides wid 21
yes,,the 2 //gms are congruent..
|dw:1350324939445:dw|
7248 congruent 6127
we just use this : 6127 is a ||gram that gives 5 is midpoint of diagonal 62
that one we already knew right ?
which one ? i thought we're trying to prove 5 is midpoint of 62 lol
whats ur question
we knew 5 was the mid point quite earlier..after that assumption, everything fitted..those 2 became congruent //gms and everything else..
no
??
those 2 became congruent || grams by construction, 5 got nothing to do wid it
let me put everything in one reply
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)
ok if that make sense good :)
so only assumption we need to prove is 36 is a median, right ?
yep..
excellency yet again..!! thank you @sauravshakya
and big thank you to @ganeshie8 ..your idea was used here after all..
+ @estudier you sparked the figure, ofcourse ! :P
I managed to get an outline of this just with algebra --- what a mess!!

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