Question

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)

Answer 1

Pythagorean triples are 3 whole numbers which satisfy the Pythagorean theorem when they make up the sides of a right angled triangle.
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,
=

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).


289 = 225 + 64
289 = 289
Since 8, 15 and 17 satisfy the criteria, they are also Pythagorean triples.