Given a and b unit vectors

Question

if |a+b|=square root 3, determine (2a-5b)dot(b+3a)

First I foiled the whole thing:
=2(a dot b)+ 6 (a dot a) - 5(b dpt b) -15(a dot b)
=-13(a dot b) + 6(a dot a) - 5(b dot b)
=-13(1)(1)+6-5
=-13+1
=-12
Textbook answer is -11/2

I don't know how to solve this problem! How do I get |a+b| and what do I do with the square root of 3?