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,
\(H^2 = B^2+P^2\\H^2 = 10^2 =100\\B^2+P^2=1^2+3^2 = 1+9 = 10\\100
eq 10\)
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,
\(H^2 = B^2+P^2\\H^2 = 9^2 =81\\B^2+P^2=4^2+5^2 = 16+25 = 41\\81
eq 41\)
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,
\(H^2 = B^2+P^2\\H^2 = 41^2 =1681\\B^2+P^2=9^2+40^2 = 81+1600 = 41\\1681= 1681\)
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,
\(H^2 = B^2+P^2\\H^2 = 44^2 =1936\\B^2+P^2=16^2+30^2 = 256+900=1156\\1936
eq 1156\)
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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