Question

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! (5 points)

Answer 1

Step-by-step explanation:

We know that the Pythagorean theorem is represented in the formula:

a^2 + B^2 = c^2

Where a and b are the legs of a right triangle, and c is the hypotenuse. Therefore, looking at the Pythagorean triples, we can infer that they are considered Pythagorean triples because they follow the Pythagorean theorem. To check if this is true, we can insert the numbers into theorem:

a^2 + b^2 = c^2

6^2 + 8^2 = 10^2

36 + 64 = 100

Since this equation is true, these three numbers could be the lengths of a right triangle, and are also therefore, a Pythagorean triple. We can also check the other three numbers:

a^2 + b^2 = c^2

5^2 + 12^2 = 13^2

25 + 144 = 169

Since this equation is also true, these three numbers could also be the side lengths of a right triangle, and are also therefore, a Pythagorean triple.