Answer:
Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.
Step-by-step explanation:
The missing options are:
<em>Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple. </em>
<em>Yes, any set of lengths with a common factor is a Pythagorean triple. </em>
<em>No, the lengths of Pythagorean triples cannot have any common factors. </em>
<em>No, the given side lengths can form a Pythagorean triple even if the lengths found in step 2 do not.</em>
A Pythagorean triple is a group of three integers (a, b and c) that satisfies the next equation:
c² = a² + b²
Multiplying the three integers by the same positive integer, you would get another Pythagorean triple.
(kc)² = (ka)² + (kb)²
k²c² = k²a² + k²b²
k²c² = k²(a² + b²)
c² = a² + b²
The procedure followed by Leon is the opposite. He found the greatest common factor and divided the given lengths by the greatest common factor, obtaining the simplest Pythagorean triple, which is (3,4,5)
