2003 Indonesia MO Problems/Problem 8
Revision as of 00:12, 11 August 2018 by Rockmanex3 (talk | contribs) (Solution to Problem 8 — Pythagorean Triples and number theory)
Problem
Given a triangle with as the right angle, and the sidelengths of the triangle are integers. Determine the sidelengths of the triangle if the product of the legs of the right triangle equals to three times the perimeter of the triangle.
Solution
Let and be the legs of the triangle. We can express the comparison as an equation. We can manipulate the equation to find a relationship between and Since we can divide both sides by without affecting the solution. We can use Simon's Favorite Factoring Trick to find integral solutions. From the equation, we find that the three possible triangles can have the following side lengths:
See Also
2003 Indonesia MO (Problems) | ||
Preceded by Problem 7 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 | Followed by Last Problem |
All Indonesia MO Problems and Solutions |