Question

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

Answer 1

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

Answer 2

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