In a triangle, the lengths of sides are 6 units, 12 units and x units. How many possible integer values are there for x?

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For three sides to form a triangle, the triangle inequality must hold for all three pairs: 1) x + 6 > 12 => x > 6 2) x + 12 > 6 => x > -6 (always true since x is positive) 3) 6 + 12 > x => 18 > x Combining these inequalities, we get: 6 < x < 18 Since x must be an integer, possible values are 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17. There are 11 integers in this range. However, the options given include 9, 10, 11, 12. The correct count is 11, but since the answer options are 9, 12, 11, 10, the correct answer is 11.

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