A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the equation a² + b² = c².

The numbers 3, 4, and 5 are a Pythagorean triple because 3² + 4² = 5². Pythagorean triples are usually written in parentheses, such as (3, 4, 5) .

You can determine other Pythagorean triples by multiplying every number in (3, 4, 5) by the same positive integer. This creates similar triangles where the number you multiplied every triple by is the scale factor.

To create Pythagorean triples that are not similar to a triangle with side lengths of 3, 4, and 5, follow these steps.

Choose two positive integers, m and n, where m>n .
Determine a using a=m2−n2 .
Determine b using b=2mn .
Determine c using c=m2+n2

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Write the triple (a, b, c) .

a. What Pythagorean triple results when m = 3 and n = 2? Explain.

b. Determine two other Pythagorean triples by multiplying every triple in part a by the same number.

c. Choose your own values for m and n. What Pythagorean triple results? Explain.