Question

If 3, 9 and x represent the lengths of the sides of a triangle, how many integer values for x are possible?

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Answer 1

As the sum of two sides of a triangle cannot be smaller than the third side, we have,
x < 9 + 3
or, x < 12
Also, as the difference of two sides of a triangle cannot be greater than the third side, we have,
x > 9 - 3
or, x > 6
Thus, the permissible values of x are 7, 8, 9, 10 and 11, i.e., 5 values.