year 8 maths

Investigation
187
Pythagorean triads and spreadsheets
Pythagorean triads (or triples) can be grouped into families. The triad (3, 4, 5) is the base triad for the
family of triads (3k, 4k, 5k) . Here are some triads in this same family.
k 1 2 3
Triad (3, 4, 5) (base triad) (6, 8, 10) (9, 12, 15)
1 Write down three more triads in the family (3k, 4k, 5k) .
2 Write down three triads in the family (7k, 24k, 25k) .
3 If (3k, 4k, 5k) and (7k, 24k, 25k) are two triad families, can you find three more families that have
whole numbers less than 100 ?
4 Pythagoras discovered that if the smaller number in a base triad is a , then the other two numbers in the
triad are given by the rules :
1
1
2 (a2 + 1) and
2 (a2 − 1)
Set up a spreadsheet to search for all the families of triads of whole numbers less than 200. Here is
how a spreadsheet might be set up.
Fill down far enough so that c is a maximum of 200 .
5 List all the base triads that have whole numbers (less than 200 ). How many are there?
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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