Step-by-step explanation:
the altitude makes a right angle at hypotenuse
cd^2+ ad^2 = ac^2
36+ (h/5)^2 = ac^2
ad/ab = 1/5; ad/h = 1/5; ad=h/5
similarly
bd^2+cd^2 = bc^2
(4/5)^2+ 36 = bc^2
ac^2+bc^2 = ab^2
36+h^2/25+ 16/25h^2+36 = h^2
h= 15
bd/ab = 4/5
bd= .8*15=12
