Lời giải:
Áp dụng định lí Pytago,ta có:
$AB^2=AH^2+HB^2$
$<=>13^2=12^2+HB^2$
$=>HB^2=13^2-12^2$
$=>HB^2=25$
$=>HB=5(cm)$
$AC^2=AH^2+HC^2$
$<=>AC^2=12^2+16^2$
$=>AC^2=400$
$=>AC=20(cm)$
Ta có:
$BC=BH+HC=5+16=21(cm)$
Chu vi tam giác $ABC$ là:
$13+21+20=54(cm)$