1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

B Pythagorean triples that sum to 60

  1. Jul 18, 2016 #1
    I'm trying to find pythagorean triples that sum to 60. Just from memory, I kow that 3-4-5 and 5-12-13, scaled to some factor, will give triples that sum to 60. These seem to be the only ones that sum to 60, but how can I be sure that there aren't more triples that sum to 60?
     
  2. jcsd
  3. Jul 18, 2016 #2

    fresh_42

    Staff: Mentor

    What do you mean by "sum up"? I don't see the ##60##.
    You can find all by ##x = u^2 - v^2 \; , \; y = 2uv \; , \; z = u^2 + v^2##.
     
  4. Jul 18, 2016 #3
    Let [itex]x,y,z[/itex] be the side lengths of a triangle you describe, so that [itex]x^2+y^2=z^2[/itex] and [itex]x+y+z=60[/itex]. You can solve for [itex]z[/itex] in the last equation and plug it into the first, getting [itex]x^2+y^2=(60-(x+y))^2=3600-120(x+y)+x^2+2xy+y^2[/itex]. This gives the equation [itex]60x+60y-xy=1800[/itex], which you can rearrange into [itex](60-x)(60-y)=1800[/itex]. Now you just need to look for positive factor pairs of [itex]1800[/itex] with both factors smaller than [itex]60[/itex] (since [itex]0<x,y<60[/itex]).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Pythagorean triples that sum to 60
  1. Pythagorean triples (Replies: 5)

  2. Pythagorean tripple (Replies: 10)

  3. Pythagorean Proof (Replies: 10)

Loading...