Maximum Length of Side AC in Triangle

In triangle ABC, the lengths of sides AB, BC, and CA are respectively represented as $a$, $b$, and $c$. If the perimeter of triangle ABC is 30, and the length of side BC is given as $b = 12$, what is the maximum possible length of side AC ($c$) given that triangle ABC must adhere to the triangle inequality conditions?

The triangle inequality states that the sum of the lengths of any two sides must be greater than the length of the remaining side. Therefore, the inequalities that need to be satisfied are:

• $a + b > c$
• $a + c > b$
• $b + c > a$

Given that the perimeter is defined as $a + b + c = 30$, you can express $a$ in terms of $c$:

$a = 30 - b - c = 30 - 12 - c = 18 - c$

Using these relationships, find the maximum possible length of side AC, $c$.