In right triangle ABC shown in the diagram below, altitude BD isdrawn to hypotenuse AC, CD = 12, and AD = 3.What is the length of AB?
Triangle ADB is similar to triangle BDC
So
AD / DB = DB / DC
3 / DB = DB / 12 cross-multiply
12 * 3 = DB * DB
36 = DB^2
DB = 6
AB = sqrt (DB^2 + AD^2) = sqrt ( 6^2 + 3^2) = sqrt ( 45) = sqrt (9 ) * sqrt (5) = 3sqrt (5)
