Question

which is/are a pythagorean triple(s)? (select all that apply.) 8, 17, 19; 9, 40, 41; 5, 12, 13; 7, 23, 24

Explanation:

A Pythagorean triple satisfies the Pythagorean theorem \(a^2 + b^2 = c^2\), where \(c\) is the largest number.

Step1: Check 8, 17, 19

Calculate \(8^2 + 17^2\) and \(19^2\).
\(8^2 = 64\), \(17^2 = 289\), so \(8^2 + 17^2 = 64 + 289 = 353\).
\(19^2 = 361\).
Since \(353
eq 361\), 8, 17, 19 is not a Pythagorean triple.

Step2: Check 9, 40, 41

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

Step3: Check 5, 12, 13

Calculate \(5^2 + 12^2\) and \(13^2\).
\(5^2 = 25\), \(12^2 = 144\), so \(5^2 + 12^2 = 25 + 144 = 169\).
\(13^2 = 169\).
Since \(169 = 169\), 5, 12, 13 is a Pythagorean triple.

Step4: Check 7, 23, 24

Calculate \(7^2 + 23^2\) and \(24^2\).
\(7^2 = 49\), \(23^2 = 529\), so \(7^2 + 23^2 = 49 + 529 = 578\).
\(24^2 = 576\).
Since \(578
eq 576\), 7, 23, 24 is not a Pythagorean triple.

Answer:

B. 9, 40, 41, C. 5, 12, 13