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Triangles with rational area



A triangle has side lengths a, b and c. We are told that its area is rational.

Which of the following can we conclude about its sides?

  1. All three sides are rational
  2. Two of the sides are rational, the third is not.
  3. One side is rational, the other two are not.
  4. None of the sides is rational.
  5. All of the above are possible.
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