questioner wrote:

There is an error in explanation of Statement 2, : 8, 10 and 12 are not Pythagorean triplets.

When we use Statement (2)

*alone* we do not know if the triangle is a right triangle or not. Such information is given in Statement (1).

So when you consider Statement (2) after you have just considered Statement (1) remember to "forget" information from Statement (1).