Question

can someone explain me this?
We refer to sets of whole numbers that satisfy the Pythagorean theorem as Pythagorean triples. The 3, 4, 5 right triangle is an example of a right triangle that uses a Pythagorean triple (32 + 42 = 52). Any multiple of a Pythagorean triple also works, such as the 6, 8, 10 and 9, 12, 15 right triangles, and so on. Some other Pythagorean triples are 5, 12, 13 and 8, 15, 17.

Answer 1

(32 + 42 = 52) means \[(3^{2 } + 4^{2} = 5^{2})\]

Answer 2

The Pythagorean theorem states that In a right triangle, the square of the hypotenuse is equal to the sum of square of two legs. The triples 3, 4, 5 and 5, 12, 13 and 8, 15, 17 and many more others triples are satisfied the condition a^2 + b^2 = c^2. Therefore, they are called the Pythagorean Triples. Please keep in mind that they are the ratios of the three sides of a right triangle. It means that their multiples such as 6, 8, 10 and 9, 12, 15 are also considered as Pythagorean triples.

Answer 3

ok, i see the relation between 3, 4, 5; 6, 8, 10 and 9, 12, 15, but not 5, 12, 13 and 8, 15, 17 :S

Answer 4

5^2+12^2=13^2
25+144=169
169=169 This means 5,12,13 is a right triangle.

Answer 5

5,12,13 and 8,15,17 are other sets of pythagorean triples. the other ones were just factors of the pythagorean triple 3,4,5

Answer 6

8^2+15^2=17^2
64+225=289
289=289 Also 8,15,17 is a right triangle cause the two sides equal the hypotenuse.

Answer 7

ohh got it, thanks :)

Answer 8

No prob. :)