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 Area Ascertainment II (Posted on 2014-10-24)
In triangle ABC, it is known that AB = 9 and BC/AC = 40/41.

Find the maximum possible area of the triangle ABC.

 No Solution Yet Submitted by K Sengupta Rating: 4.0000 (1 votes)

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 re(2): Nice problem | Comment 5 of 8 |
(In reply to re: Nice problem by Bractals)

To be quite honest I started out with a 'Heron' solution, and only in the course of that saw the key features of the problem, leading to the 'simpler' solution.

When an expression like:

1/4((-(2n-1)^8+2(2n-1)^4(2(n^2-n))^4+4(2n-1)^4(2(n^2-n))^2(2(n^2-n)+1)^2+2(2n-1)^4(2(n^2-n)+1)^4-(2(n^2-n))^8+2(2(n^2-n))^4(2(n^2-n)+1)^4-(2(n^2-n)+1)^8)/(2n-1)^4)^(1/2)

simplifies to n(n-1)(2n^2-2n+1) (i.e.) bc/2, there just has to be an easier way!

 Posted by broll on 2014-10-25 09:04:35

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