Integer Right Triangles

 Another kind of special right triangle is an "integer right triangle."  That is a right triangle whose side-lengths are whole numbers.  The converse of the Pythagorean Theorem happens to be true (and can easily be proved from SSS).  That is, if the sides of a triangle are a, b and c, and  then the triangle is a right triangle.  When a, b and c are whole numbers then the triangle is an integer right triangle and the triple (a, b, c) is called a "Pythagorean Triple," as you learned in Lesson 2.

 The most "primitive" Pythagorean triple is (3, 4, 5).  Any common multiple of these numbers is also a Pythagorean triple.  That is, if k is any whole number, then (3k, 4k, 5k) is a Pythagorean triple, because:      

                                               

                                               

For example, (6, 8, 10) and (9, 12, 15) are Pythagorean triples.

 Other Pythagorean triples are (5, 12, 13), (8, 15, 17) and (7, 24, 25).  In fact, if m and n are whole numbers and m > n, then  is a Pythagorean triple, as can be verified using algebra.

toc | return to top | previous page | next page