BD=3 CM
BC=12
AB=?
Teorema catetei

BD_l_ BC   !!
AB^2 =BD*BC
AB^2 =3*12
AB^2 =36
AB =6 cm

[tex] In~\triangle~ABC: \\ \\ m(\angle~A) =90^{o} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: AD \perp BC \\ \\ \it \overset{\text{T.C.}}{\Longrightarrow} \boxed{AB=\sqrt{BC \cdot BD}} = \sqrt{12 \cdot 3} = \sqrt{36} = 6 \: cm \\ \\ \\ \overset{\text{T.C.}}{\Longrightarrow} \boxed{AB^{2}=BC \cdot BD} = > AB^{2} = 12 \cdot 3 = > AB^{2} = 36 = > AB^{2} = {6}^{2} = > AB = 6 \: cm[/tex]