Answer: Leon was wrong by using the greatest common factor to determine that the numbers are a Pythagorean triple.
Step-by-step explanation: The numbers that Leon used in his calculations which are, 21, 28, and 35 are actually a Pythagorean triple and this can be determined by using the Pythagoras' theorem which states that,
AC² = AB² + BC²
Where AC is the longest side, and AB and BC are the other two sides.
Substituting for the given values, we now have
35² = 28² + 21²
1225 = 784 + 441
1225 = 1225
Since both sides of the equation are equal, we can conclude that the numbers form a Pythagorean triple.
However, dividing the numbers by their greatest common factor does not prove that it is a Pythagorean triple. This process cannot be successfully applied to other Pythagorean triples, and is best described as a chance event.
For example, the numbers 21, 20 and 29 are Pythagorean triples and they have no common factor. Similarly, 6, 8 and 10 are also Pythagorean triples and their greatest common factor is 2. This too is not sufficient to prove that they form a Pythagorean triple.
The only prove that is sufficient enough is to substitute the numbers into the Pythagoras theorem as stated in the calculation above, and the result must show the left hand side of the equation to be equal to the right hand side of the equation.
