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The length of three medians of a triangle are $9$,$12$ and $15$cm.The area (in sq. cm) of the triangle is

a) $48$

b) $144$

c) $24$

d) $72$

I don't want whole solution just give me the hint how can I solve it.Thanks.

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@labbhattacharjee Thanks I got a new formula. –  iostream007 May 19 '13 at 5:40
    
You can also use Appolonius theorem. –  Aryabhata May 19 '13 at 5:43
    
@iostream007, welcome. Have you tried proving it? –  lab bhattacharjee May 19 '13 at 5:44
    
i'm trying to solve it then i'll try how to prove it. Isn't any formula to the same because this question asked in SSC exam and there is not so much to spent on 1 question? –  iostream007 May 19 '13 at 5:48
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2 Answers 2

You know that medians divide a triangle to 6 equal areas. If you find one of them, multiplying with 6 give you the area of whole triangle. Let's denote one area as $S$, now see the figure: enter image description here

I guess you saw the right triangle.

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What right triangle? Can you please elaborate? –  Aryabhata May 19 '13 at 6:05
    
the triangle of 6-8-10. We get this by drawing paralels, 6 to 6, 10 to 10. –  nikamed May 19 '13 at 6:06
    
Thanks! I see it now :-) +1. –  Aryabhata May 19 '13 at 6:08
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there is a direct formula. let s be there. s= (m1+m2+m3)/2 area= square_root(s*(s-m1)(s-m2)(s-m3));

this gives answer of above ques as 72.

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