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Appropriate Area (Posted on 2007-03-21) Difficulty: 3 of 5
Consider a triangle with sides of length 5, 6, 7. If you square the area of that triangle, you get 216, a perfect cube.

Are there other triangles (not geometrically similar to the first triangle) with integral sides whose area squared is a perfect cube? Find one such triangle, or prove no others exist.

No Solution Yet Submitted by Gamer    
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re: Solution Comment 4 of 4 |
(In reply to Solution by Bractals)

Very nice!

The solution generator you gave (2k+1, k^2+k, k^2+k+1) is linearly independent over second degree polynomials, which proves that all the triangles generated by different values of k will all be non-similar and that there is an infinite number of nontrivial solutions!


  Posted by Brian Smith on 2007-03-22 14:01:04
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