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Pythagorean Triples

Part of the Triangles section of Coddy's Geometry journey. Lesson 25 of 63.

A few right triangles have whole-number sides all round. Those sets of three numbers are Pythagorean triples. The ones worth knowing by heart are 3, 4, 5 and 5, 12, 13 and 8, 15, 17.

Any multiple of a triple is a triple too. Doubling 3, 4, 5 gives 6, 8, 10, and 6^2 + 8^2 = 10^2 because every square grows by the same factor 4. Tripling gives 9, 12, 15.

$Right triangle PQR with legs 12 and 9$

So when you see legs 9 and 12, notice they are 3 and 4 times 3: the hypotenuse is 5 times 3, which is 15. The theorem gives the same answer, and spotting the triple is a quick check on it.

Challenge

△ABC has a right angle at A. Find the hypotenuse BC, then press Check. Before you check, see which triple the legs belong to.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Triangles

2The Triangle Inequality

Can Three Sticks Meet?Exactly Reaching The Range of the Third Side The Formula Recap: The Third Side

5The Pythagorean Theorem

Squares on the Sides Finding the HypotenusePythagorean TriplesWhen It Is Not Whole Recap: The Hypotenuse

8Special Right Triangles

The 45-45-90 Triangle Legs from the Hypotenuse The 30-60-90 Triangle All Three Sides Which Triangle Is It?Recap: Special Triangles

11Two Tools at Once

Height of an Isosceles Area from the Height The Equilateral Triangle Right Triangle Perimeter Recap: Two Tools