When a perpendicular is dropped from the right-angle (C) to the opposite side AB, the metric relations apply: BD*BA=a^2 ..........................(1) AD*AB=b^2...........................(2) BD*DA=DC^2........................(3)
Given AD=6, AB=24, using metric relation (2) above, we have b^2=6*24=144 => b=sqrt(144)=12
By the way, we conclude that this is a 30-60-90 triangle because b/AB=(1/2)=sin(B) => B=30 degrees.
