$a)$ Xét $ΔABC$ vuông tại $A$ , đường cao $AH$
$AH^2=BH.CH$
$16^2=25.CH$
$CH=10,24cm$
$BC=CH+BH=25+10,24=35,24cm$
$AB^2=BH.BC$
$AB^2=25.35,24$
$AB^2=881$
$AB=29,68cm$
$AC^2=CH.BC$
$AC^2=10,24.35,24$
$AC^2=360,8576$
$AC=19cm$
$b)$ Xét $ΔABC$ vuông tại $A$ , đường cao $AH$
$AB^2=BH.BC$
$12^2=6.BC$
$BC=24cm$
$AC^2=BC^2-AB^2$
$AC^2=24^2-12^2$
$AC^2=432$
$AC=20,79cm$
$CH=BC-BH=24-6=18cm$
$AH^2=BH.CH$
$AH^2=6.18$
$AH^2=108$
$AH=10,39cm$