Question

which set of side lengths is a pythagorean triple? 16, 30, 44 1, 3, 10 4, 5, 9 9, 40, 41

Explanation:

Step1: Check the Pythagorean theorem condition

For a set of three numbers \(a,b,c\) (\(c\) is the largest number), check if \(a^{2}+b^{2}=c^{2}\).

For the set \(1,3,10\):

\(1^{2}+3^{2}=1 + 9=10\), and \(10^{2}=100\). Since \(10
eq100\), this is not a Pythagorean triple.

For the set \(4,5,9\):

\(4^{2}+5^{2}=16 + 25=41\), and \(9^{2}=81\). Since \(41
eq81\), this is not a Pythagorean triple.

For the set \(16,30,44\):

\(16^{2}+30^{2}=256+900 = 1156\), and \(44^{2}=1936\). Since \(1156
eq1936\), this is not a Pythagorean triple.

For the set \(9,40,41\):

\(9^{2}+40^{2}=81 + 1600=1681\), and \(41^{2}=1681\). Since \(9^{2}+40^{2}=41^{2}\), this is a Pythagorean triple.

Answer:

\(9,40,41\)