AMC 12A 2013 Problem 12

The angles in a particular triangle are in arithmetic progression, and the side lengths are 4,5 , and x. The sum of the possible values of x equals a+\sqrt{b}+\sqrt{c}, where a, b, and c are positive integers. What is a+b+c ?

Answer Choices
A. 36
B. 38
C. 40
D. 42
E. 44