Question

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Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using this procedure.

Step 1: Find the greatest common factor of the given lengths: 7
Step 2: Divide the given lengths by the greatest common factor: 3, 4, 5
Step 3: Verify that the lengths found in step 2 form a Pythagorean triple: 3 squared + 4 squared = 9 + 16 = 25 = 5 squared

Leon states that 21, 28, 35 is a Pythagorean triple because the lengths found in step 2 form a Pythagorean triple. Which explains whether or not Leon is correct?

Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.

Yes, any set of lengths with a common factor is a Pythagorean triple.

No, the lengths of Pythagorean triples cannot have any common factors.

No, the given side lengths can form a Pythagorean triple even if the lengths found in step 2 do not.

Answer 1

Answer:

  (a)  Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.

Step-by-step explanation:

In general, scaling the numbers involved in a relationship does not change their relationship.

If we have ...

  a² +b² = c²

and we scale each number by a factor of k, then we get ...

  (ka)² +(kb)² = (kc)²

  k²a² +k²b² = k²c²

  k²(a² +b²) = k²c² . . . . same result as multiplying the original relation by k²

Leon is correct that multiplying a Pythagorean triple by a constant gives another Pythagorean triple.