Which of the following sets of side lengths forms a $\mathrm{Pythagorean} \mathrm{triple}$?

• A. $6,8,13$
• B. $2,3,4$
• C. $5,6,7$
• D. $3,4,5$

Answer: (D)

Verified step by step guidance

1. Recall that a Pythagorean triple consists of three positive integers \(a\), \(b\), and \(c\) such that \(a^2 + b^2 = c^2\), where \(c\) is the longest side (hypotenuse).
2. For each set of side lengths, first identify the largest number as the potential hypotenuse \(c\).
3. Calculate the squares of the two smaller sides and add them together: \(a^2 + b^2\).
4. Calculate the square of the largest side: \(c^2\).
5. Compare the sums: if \(a^2 + b^2 = c^2\), then the set forms a Pythagorean triple; otherwise, it does not.