All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
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    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
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
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (7)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information