Pythagorean Triples

Students learn that a Pythagorean Triple is a set of integers that satisfies the Pythagorean Theorem (a^2 + b^2 = c^2). For example, 3-4-5 is a Pythagorean Triple, because 3^2 + 4^2 = 5^2. The following sets of integers are also Pythagorean Triples: 5-12-13, 8-15-17, 7-24-25, and so on. Note that any multiple of a Pythagorean Triple is also a Pythagorean Triple. For example, since 3-4-5 is a Pythagorean Triple, then 6-8-10 is also a Pythagorean Triple. Students are then asked to find the lengths of missing sides of right triangles using Pythagorean Triples. Note that students are also asked to solve word problems that involve Pythagorean Triples, such as the following: What is the distance across the diagonal of a rectangular field that is 32 feet wide and 60 feet long?