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To find the possible length for side AB in triangle ABC with sides BC = 12 and AC = 21, we can use the triangle inequality theorem. The sum of the lengths of any two sides must be greater than the length of the third side. Therefore, we can write the inequalities:

  1. AB + BC > AC → AB + 12 > 21 → AB > 9
  2. AB + AC > BC → AB + 21 > 12 → AB > -9 (which is always true)
  3. BC + AC > AB → 12 + 21 > AB → 33 > AB or AB < 33

Combining these, we get the inequality: 9 < AB < 33.

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