By the triangle inequality theorem, if two sides of a triangle have lengths of 6 and 13, what are the possible lengths of the third side? a) 7 < x < 18 b) 7 < x < 19 c) 8 < x < 18 d) 8 < x < 19

1. You have that two sides of a triangle have lengths of 6 and 13. Then, by the Triangle Inequality Theorem, you have:

 a+b>c
 a+c>b
 b+c>a

 3. Therefore, you have:

 a=6
 b=13

 c<a+b
 c<6+13
 c<19

 4. The difference between a and b should be lesser that c. Then

 a-b<c
 13-6<c
 7<c

 5. Therefore:

 c=x

 7<x<19

 The correct answer is the option B:  B. 7<x<19

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