If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 6, and k?  Answers.
A) one
B) two
C) three
D) four
E) five
(6-2) &lt; k &lt; (6+2)   4 &lt; k &lt; 8   Thus k = 5, 6, 7   Since 2 &lt; k &lt; 7, then k can be 5 or 6.   The answer is two.
<result>B</result>
If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 6, and k?