Concept:A Pythagorean triple is a set of three positive integers $a, b,$ and $c$, such that $a^2 + b^2 = c^2$. In a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.Explanation:We need to find which set of numbers does NOT satisfy the Pythagorean theorem ($a^2 + b^2 = c^2$). We will check each option:Option A: 6, 8, 12Let $a=6$, $b=8$, and $c=12$.Check if $6^2 + 8^2 = 12^2$.$36 + 64 = 144$$100 \neq 144$. So, this is not a Pythagorean triple.Option B: 5, 12, 13Let $a=5$, $b=12$, and $c=13$.Check if $5^2 + 12^2 = 13^2$.$25 + 144 = 169$$169 = 169$. So, this is a Pythagorean triple.Option C: 6, 8, 10Let $a=6$, $b=8$, and $c=10$.Check if $6^2 + 8^2 = 10^2$.$36 + 64 = 100$$100 = 100$. So, this is a Pythagorean triple.Option D: 7, 24, 25Let $a=7$, $b=24$, and $c=25$.Check if $7^2 + 24^2 = 25^2$.$49 + 576 = 625$$625 = 625$. So, this is a Pythagorean triple.The only set of numbers that does not satisfy the Pythagorean theorem is 6, 8, 12.Answer:A. 6, 8, 12