Which of the following sets of side lengths can form a right triangle?

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

Answer: (D)

Verified step by step guidance

1. Recall that a set of side lengths forms a right triangle if and only if they satisfy the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c\) is the longest side (hypotenuse).
2. For each set of side lengths, first identify the longest side and label it as \(c\), and the other two sides as \(a\) and \(b\).
3. Calculate \(a^2 + b^2\) and compare it to \(c^2\) for each set:
4. - For example, for the set (6, 8, 10), check if \$6^2 + 8^2 = 10^2$.
5. If the equality holds true, then the set can form a right triangle; if not, it cannot.