If a=12 and b=5 what does c=

The context of this problem is pretty vague as I'm not sure what you're referring to, but, usually, if the first three letters of the alphabet are involved, I'm going to assume that this involves the Pythagorean Theorem.

Basically the Pythagorean Theorem states:

a² + b² = c²

Where a and b represent the two legs of a triangle and c represents the triangle's hypotenuse.

12² + 5² = c²

144 + 25 = c²

169 = c²

√169 = c

13 = c

Solution: c = 13