Which set of number could represent the length of the sides of a right triangle? a 9 11 14 b 15 18 21 c 7 24 25 d 8 9 10

Common Pythagorean triples include
  (3, 4, 5)
  (5, 12, 13)
  (7, 24, 25)
  (9, 40, 41)
The only Pythagorean triple that is an arithmetic sequence is (3, 4, 5), so any arithmetic sequence that is a Pythagorean triple must be a multiple of that, such as (9, 12, 15) or (15, 20, 25).

The arithmetic sequences of selections B and D are unrelated to the (3, 4, 5) triple, so cannot be Pythagorean triples. For selection A, we know that 9² + 11² = 81 + 121 = 202 > 14², so that is not a right triangle.

The appropriate selection is ...
  C. 7, 24, 25

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