Hawkeye's problem
Find the area of triangle having lengths of medians as 6 , 8 and 1 0 .
If you get this you will also get this problem .
The answer is 32.
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4 solutions
Another method :
The area of a triangle = 3 4 times the area of the triangle formed by it's medians
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Didn't Know that! Thanks!!!
i used ur method vaibhav.
Its*. 😉 Good to know that! Thanks!
awesome one nice observation man!
but how do we calculate area formed by medians??
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@Nithin Nithu , We take the lengths of the Medians to be the Sides of a triangle. And then Solve it Using Heron's formula :) :). For Example The triangle formed by the medians Of the given triangle Will have sides 6,8,10(Lengths of median).
Therefore the area of the triangle formed by the medians Is 1/2 8 6 = 24.(Because It is a right angled triangle.)
Therefore the area of the Triangle Is 4/3*24= 32.
I hope you get it now ⌣ ¨
I see it! Thanks!
Haha you didn't even change variables here Take it in good humour.
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Lol , but I read this formula in a book.Just a coincidence... xD
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Haha i searched for more formulaes about area of triangle and landed there and saw they were exactly same.Really funny coincidence.U must be laughing loud i can imagine.
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@Gautam Sharma – May be its a standard notation for median length.
@Gautam Sharma – formulae* xD
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@Nihar Mahajan – Another lol i didn't press 'e ' in formulaes it just got along with s.i wanted to write formulas.
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@Gautam Sharma – Well are you on facebook?
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@Nihar Mahajan – yeah i am on fb
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@Gautam Sharma – did you recieve my friend request? There are many sharmas on fb... even in Indian cricket team ... xD
This image was taken of another problem solved by
@Matt Enlow
. It is a proof without words.
By the lenght of the sides we know that is a rectangle triangle so its area is 2 6 × 8 = 2 4 therefore triangles' area is 3 2 4 × 4 = 3 2
Amazing Proof!
Just use the formula when u have the lengths of all medians .. (4/3) * heron's formula
reference: http://math.stackexchange.com/questions/168701/finding-the-area-of-triangle-if-length-of-medians-are-given
still working from what planet did they get that formula :)
Area of triangle A B C where u , v , w are its medians is given by :
3 1 [ 2 ( u 2 v 2 + v 2 w 2 + u 2 w 2 ) − ( u 4 + v 4 + w 4 ) ]
When u = 6 , v = 8 , w = 1 0 , Area is 3 2 .
Mehul Arora