Answer:
Option D. [tex]8,40,41[/tex]
Step-by-step explanation:
we know that
A "Pythagorean Triple" is a set of positive integers, a, b and c that fits the Pythagorean Theorem
[tex]c^{2}=a^{2}+b^{2}[/tex]
where
c is the greater length side
Verify each case
Case A) [tex]3,4,5[/tex]
[tex]5^{2}=3^{2}+4^{2}[/tex]
[tex]25=25[/tex] -----> Is true
therefore
the set of integers is a Pythagorean Triple
Case B) [tex]6,8,10[/tex]
[tex]10^{2}=6^{2}+8^{2}[/tex]
[tex]100=100[/tex] -----> Is true
therefore
the set of integers is a Pythagorean Triple
Case C) [tex]5,12,13[/tex]
[tex]13^{2}=5^{2}+12^{2}[/tex]
[tex]169=169[/tex] -----> Is true
therefore
the set of integers is a Pythagorean Triple
Case D) [tex]8,40,41[/tex]
[tex]41^{2}=8^{2}+40^{2}[/tex]
[tex]1,681=1,664[/tex] -----> Is not true
therefore
the set of integers is not a Pythagorean Triple
