2014-07-02 09:00:46

In a certain isosceles triangle, one side is 5 and one side is 13. Which of the following CANNOT be the measure of the third side?

I. 5
II. 12
III. 13

(A) I only
(B) II only
(C) I and II
(D) II and III
(E) None of the above

The correct answer is C

Explanation: The triangle must be isosceles according to the question. Thus, two sides must be identical. This means that only 5 and 13 are possibilities for the missing side, eliminating option II. 5, however, also does not work, as a 5-5-13 triangle cannot exist, as the two short sides sum to less than the third side, and a side of a triangle must be shorter than the sum of the other two sides. As this question asks for the possibilities that do NOT work, choice C is correct.