Pythagorean triples are formed by whole numbers, so that a2 + b2 = c2.
For example, the numbers 3, 4 and 5 form a Pythagorean Triple because 32 + 42 = 52. There are many Pythagorean triples. Some other examples are
5, 12, 13
8, 15, 17
7, 24, 25
If we multiply each number of a Pythagorean triple by the same number, we form another Pythagorean triple. For example 6, 8, 10 is a Pythagorean triple because it is 2(3), 2(4), 2(5).
Memorising some common Pythagorean triples can helpful.
For example, if we see that the sides of a triangle form a Pythagorean triple then we know that it is a right triangle.
The following video gives some examples of Pythagorean triples.
Pythagorean triples may also help us to find the missing side of a right triangle faster. If two sides of a right triangle form part of a triple then we can know the value of the third side without having to calculate using the Pythagorean theorem.
Example:
Find the value of x
Solution:
Check for Pythagorean triple:
Get the ratio of the two given sides:
12 : 20 = 3 : 5 ( divide by 4 )
From the ratio, we know that it is a Pythagorean triple.
So, x = 4 × 4 = 16 cm
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