Đáp án:
$\dfrac{DH}{BH} = 9$
Giải thích các bước giải:
Ta có: $ΔABH \sim ΔCAH \, (g.g)$
$\Rightarrow \dfrac{AB}{AC} = \dfrac{AH}{CH}$
$\Rightarrow \dfrac{AB^2}{AC^2} = \dfrac{AH^2}{CH^2} = \dfrac{BH.CH}{CH^2} = \dfrac{BH}{CH}$
$\Rightarrow \dfrac{BH}{CH} = \dfrac{1}{4}$
$\Rightarrow \dfrac{BH}{BC} = \dfrac{1}{5}$
$\Rightarrow \dfrac{BC}{BH} =5$
$\Rightarrow \dfrac{2BC}{BH} = 10$
Ta lại có:
$\dfrac{DH}{BH} = \dfrac{BD - BH}{BH}$
$=\dfrac{2BC - BH}{BH} = \dfrac{2BC}{BH} - 1$
$=10 - 1 =9$
Vậy $\dfrac{DH}{BH} = 9$
