a,
$\Delta$ ABC và $\Delta$ HBA có:
$\widehat{BAC}=\widehat{BHA}=90^o$
$\widehat{B}$ chung
$\Rightarrow \Delta$ ABC $\backsim$ $\Delta$ HBA (g.g) (*)
b,
$BC=\sqrt{AB^2+AC^2}= 10cm$
(*) $\Rightarrow \frac{AH}{AB}=\frac{AC}{BC}$
$\Leftrightarrow AH=\frac{AB.AC}{BC}=4,8cm$
c,
$\Delta$ ACD và $\Delta$ HCE có:
$\widehat{DAC}=\widehat{EHC}=90^o$
$\widehat{ACD}=\widehat{HCE}$
$\Rightarrow \Delta$ ACD $\backsim$ $\Delta$ HCE
$CH= \sqrt{AC^2-AH^2}= 6,4cm$
$\Rightarrow \frac{S_{ACD}}{S_{EHC}}=k^2=(\frac{8}{6,4})^2=\frac{25}{16}$