Challenging Triangle Problem

Level pending

Either number 1, 2, 3, or 4 is a correct statement. Choose which statement is correct.

Given triangle ABC with integer side lengths a and b and integer area K, side c is an integer if an only if

  1. (ab+2K)(ab-2K) is a perfect square
  2. (ab^2c^3)/K is a multiple of 6
  3. a and b are divisible by K
  4. side c is equal to 8

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