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The sets of numbers 6, 8, 10 and 5, 12, 13 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!

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Answer:We know that the Pythagorean Theorem is a² + b² = c².  First lets start with 6, 8, and 10. There is a simple way to know that these are Pythagorean triples. They make up what is called a 3-4-5 triangle. 3 x 2 is 6, 4 x 2 is 8, and 5 x 2 is 10. Next 5, 12, and 13 are Pythagorean triplets because 5² + 12² = 13². Because both of these form right triangles, we know that they are Pythagorean triplets.

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Step-by-step explanation:

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The Pythagorean triples are those three numbers of which the square of a number is the sum of the squares of the other two numbers.

What is Pythagorean Theorem?

According to the Pythagoras theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the base and height.

Given, three numbers are 6, 8, 10.

It is clear that, 6² + 8² = 36 + 64 = 100 = 10². Therefore, these three numbers are Pythagorean triples. Hence, for a right-angled triangle, the hypotenuse is 10 and other two sides are 6 and 8 respectively.

Again, three numbers given: 5, 12, 13.

It is also clear that, 5² + 12² = 25 + 144 = 169 = 13².Therefore, these three numbers are Pythagorean triples. Hence, for a right-angled triangle, the hypotenuse is 13 and other two sides are 12 and 5 respectively.

Learn more about the Pythagorean Theorem here: https://brainly.com/question/16426393

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