shubhamsrg
  • 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 ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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shubhamsrg
  • shubhamsrg
or,,prove that this ratio always equals 4/3
anonymous
  • anonymous
im watching :)
anonymous
  • anonymous
|dw:1350313254678:dw|

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

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