In the following figure, AF is the perpendicular bisector of BD, AD = 30, and DF = 12. Find AB + BF.
Since AF is the perpendicular bisector both angle(AFD) and angle(AFB) are right angles;
also, BF is congruent to DF.
Since AF is congruent to AF, triangle(ABF) is congruent to triangle(ADF) --- side-angle-side.
Therefore, AD = AB = 30 and DF = BF = 12.
You can now calculate AB + BF.