Which of the following sets of numbers could represent the three sides of a right triangle?

• A. $7$, $24$, $25$
• B. $2$, $2$, $3$
• C. $5$, $6$, $10$
• D. $3$, $4$, $5$

Answer: (D)

Verified step by step guidance

1. Recall that for three numbers to represent the sides of a right triangle, they must satisfy the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c\) is the longest side (hypotenuse).
2. Identify the longest side in each set of numbers, as this will be the candidate for the hypotenuse.
3. For each set, square the two shorter sides and add them 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. If they are equal, the set can represent the sides of a right triangle.
5. Apply this process to each given set: (7, 24, 25), (2, 2, 3), and (5, 6, 10), to determine which satisfy the Pythagorean theorem.