The only Pythagorean triple is c.
Pythagorean triple
A Pythagorean triple is a set of positive integers that follows the Pythagorean theorem.
Given to us
A.1, 3, 10
B.4, 5, 9
C.9, 40, 41
D.16, 30, 44
Solution
A.) 1, 3, 10
H = 10, as 10 is the largest number in the set,
[tex]H^2 = B^2+P^2\\H^2 = 10^2 =100\\B^2+P^2=1^2+3^2 = 1+9 = 10\\100\neq 10[/tex]
As we can see that the square of the biggest number is not equal to the sum of the square of the other two numbers.
B.) 4, 5, 9
H = 9, as 9 is the largest number in the set,
[tex]H^2 = B^2+P^2\\H^2 = 9^2 =81\\B^2+P^2=4^2+5^2 = 16+25 = 41\\81\neq 41[/tex]
As we can see that the square of the biggest number is not equal to the sum of the square of the other two numbers.
C.) 9, 40, 41
H = 41, as 41 is the largest number in the set,
[tex]H^2 = B^2+P^2\\H^2 = 41^2 =1681\\B^2+P^2=9^2+40^2 = 81+1600 = 41\\1681= 1681[/tex]
As we can see that the square of the biggest number is equal to the sum of the square of the other two numbers.
D.) 16, 30, 44
H = 44, as 44 is the largest number in the set,
[tex]H^2 = B^2+P^2\\H^2 = 44^2 =1936\\B^2+P^2=16^2+30^2 = 256+900=1156\\1936\neq 1156[/tex]
As we can see that the square of the biggest number is not equal to the sum of the square of the other two numbers.
Hence, the only Pythagorean triple is c.
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