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Question

The lengths of the sides of a non-degenerate triangle are x, 13 and 37 units. How many integer values of x are possible?

Accepted Answer

By the triangle inequality, align* x + 13 &> 37, x + 37 &> 13, 13 + 37 &> x, align* which tell us that x > 24, x > -24, and x < 50. Hence, the possible values of x are 25, 26, , 49, for a total of 49 - 25 + 1 = 25.