Which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle?

For a triangle with longest side c, it is obtuse when the squares of the other two sides add to less than c². For 8, 10, and 14, the triangle inequality holds because 8 + 10 > 14, and 8² + 10² = 164 < 14² = 196. So 8, 10, and 14 can be the side lengths of an obtuse triangle.

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