Question

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

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

Explanation:

Another example of multiplying a Pythagorean triple is

Take the known Pythagorean triple 5, 12 and 13:

5 12 13 * 2 = 10 24 26

and 26^2 = 10^2 + 24^2

676 = 100 + 576 = 676