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Pythagorean Triads
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Transcript
Here's a list of a few
Pythagorean Triads...
- (3,4,5)
- (5,12,13)
- (7,24,25)
- (8,15,17)
- (9,40,41)
- (11,60,61)
- (12,35,37)
there are many more....
What is a Pythagorean Triad?
When the side lengths of a right triangle satisfy the Pythagorean theorem, these three numbers are known as Pythagorean triad.
What is the relationship between these Pythagorean Triads?
- (3,4,5)
- (6, 8, 10)
- (9, 12, 15)
Example of a Pythagorean Triad
The most common example of Pythagorean triad are 3,4,5 triangles.
A 3,4,5 triad simply stands for a triangle that has a side of length 3, a side of length 4 and a side of length 5.
If a triangle has these side lengths, then it MUST be a right triangle.
The set of Pythagorean Triples is endless.
We can prove this with the help of the first
Pythagorean Triple (3, 4, and 5):
Year 9 Maths
Pythagorean Triads
How can we check if 3 numbers form a Pythagorean Triad?
Let's try 5, 12, 13....
5^2 + 12^2 = 13^2
25 + 144 = 169
169 = 169
Therefore, 5, 12, 13 is a triad
Try one for yourself...
9, 40, 41
References:
- http://www.mathsisfun.com/numbers/pythagorean-triples.html
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