Which of the following sets of side lengths can form a right triangle according to the $\mathrm{Pythagorean} \mathrm{Theorem}$?

• A. $2$, $2$, $3$
• B. $5$, $6$, $7$
• C. $6$, $8$, $10$
• D. $3$, $4$, $5$

Answer: (D)

Verified step by step guidance

1. Identify the longest side in each set of side lengths, as this will be the hypotenuse candidate in the right triangle.
2. Apply the Pythagorean Theorem, which states that for a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\), the relationship \(a^2 + b^2 = c^2\) must hold true.
3. For each set, square the two shorter sides and add their squares together, then square the longest side separately.
4. Compare the sum of the squares of the two shorter sides to the square of the longest side for each set:
5. If the sums are equal for a set, then that set of side lengths can form a right triangle according to the Pythagorean Theorem.