Select the set in which the relationship among the three numbers is the same as that in the given set (5, 12, 13).

Question

Select the set in which the relationship among the three numbers is the same as that in the given set (5, 12, 13).

1. A. (3, 10, 14)
2. B. (7, 26, 28)
3. C. (3, 4, 5) (Correct answer)
4. D. (9, 10, 12)

Correct Answer

Option C — (3, 4, 5)

Detailed Solution & Explanation

The correct answer is (3, 4, 5).

Key Points

• In the given set, 5² + 12² = 25 + 144 = 169 = 13². The three numbers form a Pythagorean triple.
• Test option C: 3² + 4² = 9 + 16 = 25 = 5². It is also a Pythagorean triple, so the relation matches.

Additional Information

• (3, 10, 14): 9 + 100 = 109, but 14² = 196 — not a triple.
• (7, 26, 28): 49 + 676 = 725, but 28² = 784 — not a triple.
• (9, 10, 12): 81 + 100 = 181, but 12² = 144 — not a triple.
• The smallest primitive Pythagorean triples are (3,4,5), (5,12,13), (8,15,17), (7,24,25) and (20,21,29); recognising them on sight saves time.

*Ministry of Papers worked solution. The Commission has not yet published the official key for this paper; this answer will be reconciled with it on release.*