Testing for Pythagorean Triads

A Pythagorean triad is a set of three whole numbers, such as \((5, 12, 13)\), where the squares of the two smaller numbers add up to the square of the largest. In NSW Year 8 maths, triads give right-angled triangles whose sides are all whole numbers (NESA outcome MA4‑PYT‑C‑01).

You will test sets of numbers, including sets not written in order, and give a reason for each answer. You will find a missing number in a triad, build new triads by multiplying \((3, 4, 5)\) or \((8, 15, 17)\) by a whole number, and see why adding two triads does not work. Tilers and landscapers use triads to set out square corners with no rounding. It is part of Year 8 Pythagoras.