Question 286011
If by perfect triple is meant Pythagorean triple, we must have the following criteria met (there are more but these should be more than sufficient...):

a^2+b^2=c^2

a=s^2-t^2
b=2st
c=s^2+t^2

with s,t integers. (Note: a and b are interchangeable, IE it doesn't matter which comes first in the first equation.) There are also interesting properties of s and t that one could investigate if interested.

Additionally, |a+b|<=|a|+|b|. IE the hypotenuse is less than or equal to the sum of the legs. This criteria is met by your three numbers, so we must investigate further with the first equation [easiest to do].

The question is: is 6^2+8^2=10^2?
IE is 36+64=100? Yes.

The last two lines are sufficient to understand the concept, but I hope you see there are many more relationships to note with Pythagorean triples than may be presented in a basic algebra or geometry text.