Đặt $AB=5x(cm); AC=12x(cm)$ ($x>0$)
Theo Pytago:
$(5x)^2+(12x)^2=26^2$
$\to x^2=4$
$\to x=2$
$\to AB=10(cm); AC=24(cm)$
Theo hệ thức lượng:
$AH=\dfrac{AB.AC}{BC}=\dfrac{120}{13}(cm)$
$BH=\dfrac{AB^2}{BC}=\dfrac{50}{13}(cm)$
$CH=\dfrac{AC^2}{BC}=\dfrac{288}{13}(cm)$