Results 1 to 2 of 2

Math Help - triangle with integer sides

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    69

    Question triangle with integer sides

    how can you find all right-angled triangle with integer sides if one of the sides is 2001 units long?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by Intsecxtanx View Post
    how can you find all right-angled triangle with integer sides if one of the sides is 2001 units long?
    2001 is pretty small. You can generate all primitive Pythagorean triples until an upper bound, and use the prime factorization of 2001 when considering which multiples could lead to a side length of 2001. Look on Wikipedia for how to generate Pythagorean triples.

    Edit: Actually, generating all the triples is probably overkill in this case, although it probably involves the least thought.

    Using the equations from the Wikipedia page, you can set one of a, b, c equal to 2001. Obviously, 2mn can't equal 2001 or any of its factors. For the other two, you might want to use Dario Alpern's online quadratic Diophantine solver. (The link is the JavaScript version, I believe. A faster version is a Java applet but the speed increase won't be noticeable for such small numbers.)

    Edit 2: The only factor of 2001 that could equal m^2 + n^2 is 29. See here.

    (Edited a mistake out too.)

    Edit 3: m^2 - n^2 can be written (m-n)(m+n) which reduces it to a factorization problem.
    Last edited by undefined; April 22nd 2010 at 11:20 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Isosceles Triangle With Integer Sides
    Posted in the Number Theory Forum
    Replies: 7
    Last Post: May 12th 2010, 10:27 AM
  2. Suppose we have a right triangle with integer sides
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: April 19th 2010, 06:39 PM
  3. Consider a right triangle with integer sides...
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: April 19th 2010, 06:34 PM
  4. sides of triangle
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: December 6th 2009, 10:11 AM
  5. Replies: 7
    Last Post: July 19th 2008, 06:53 AM

Search Tags


/mathhelpforum @mathhelpforum