The sets of numbers 3, 4, 5 and 8, 15, 17 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain or show why they are Pythagorean triples. Be sure to show your work for each set of triples! (5 points)

For the numbers 3, 4 and 5, let 5 be the length of the hypotenuse (AC, of triangle ABC in which B is a right angle), and 4 and 3 be the lengths of the other 2 sides of the triangle (AB and AC).

According to the Pythagorean theorem,

[tex]AC^{2}[/tex] = [tex]AB^{2} + BC^{2}[/tex]

[tex]5^{2} = 3^{2} + 4^{2}[/tex]

25 = 9 + 16

25 = 25

Since 3, 4 and 5 satisfy the criteria, they are Pythagorean triples.

Similarly, for the numbers 8, 15 and 17, let 17 be the length of the hypotenuse (PR, of triangle PQR in which Q is a right angle), and 4 and 3 be the lengths of the other 2 sides of the triangle (PQ and QR).

[tex]PR^{2} = PQ^{2} + QR^{2}[/tex]

[tex]17^{2} = 15^{2} + 8^{2}[/tex]

289 = 225 + 64

289 = 289

Since 8, 15 and 17 satisfy the criteria, they are also Pythagorean triples.

oeerivona oeerivona · Answer 2 · 2021-10-29T12:18:15+02:00

A Pythagorean triple is a set of three numbers, x, y, and z, such that the

relationship between them is; x² + y² = z²

The three numbers 3, 4, and 5 are a Pythagorean triple, because, we have;

3² + 4² = 25 = 5²

Similarly, the set of numbers, 8, 15, and 17 are Pythagorean triple given that

we have;

8² + 15² = 289 = 17²

Therefore, 8, 15, and 17 are Pythagorean triples, given that the sum of the

square of two smaller numbers gives the square of the larger number.

An general form of the triple is (2·x)² + (x² - 1)² = (x² + 1)²

Learn more here:

https://brainly.com/question/11279692