Pythagorean Triples
Part of the Triangles section of Coddy's Geometry journey. Lesson 31 of 71.
Some right triangles have three sides that are all whole numbers. Such a set of three numbers is a Pythagorean triple. The smallest triple is 3, 4, 5. The next ones are 5, 12, 13, then 8, 15, 17, then 7, 24, 25. Each triple satisfies the theorem exactly. For example, 5^2 + 12^2 = 25 + 144 = 169 = 13^2.
If you multiply every side of a Pythagorean triple by the same whole number, you get another triple. For example, doubling 3, 4, 5 gives 6, 8, 10. Each square is multiplied by the same factor, so the equation still holds. So if the legs are 6 and 8, the hypotenuse is 10. When the legs do not belong to a triple, find the hypotenuse the usual way: square the legs, add, and take the root.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Triangles
1Sides and Names
Three Sides, Three CornersSorting by SidesNaming by AnglesTicks into EquationsThe Longest SideRecap: Sorting Triangles2The Triangle Inequality
Can Three Sticks Meet?Exactly ReachingHow Short Can It Be?How Long Can It Be?The Range of the Third SideThe FormulaWhole-Number SidesRecap: The Third Side5The Hypotenuse
Squares on the SidesFinding the HypotenusePythagorean TriplesWhen It Is Not WholeSimplifying the RootRecap: The Hypotenuse8Special Right Triangles
The 45-45-90 TriangleLegs from the HypotenuseThe 30-60-90 TriangleAll Three SidesWhich Triangle Is It?Recap: Special Triangles11Mixing Area and Pythagoras
Height of an IsoscelesArea from the HeightThe Equilateral TriangleRight Triangle PerimeterRecap: Two Tools3Perimeter
Around the EdgeA Missing SideIsosceles PerimeterEquilateral PerimeterSides as ExpressionsWrite the PerimeterRecap: Around the Edge6Finding a Leg
Working BackwardsThe LadderWhich Side Is c?A Leg That Is Not WholeRecap: Finding a Leg