Find length of side

Question

I tried to solve this problem ... but i can't find answer.

Anyone can help me?

EBC=90 & DCB=90 & AHC=AHB=90

Answer 1

The problem is ill-posed. Notice that $\Delta EBC \sim \Delta AHC$ and $\Delta DCB \sim \Delta AHB$. Thus,

$\frac{2}{BC} = \frac{1}{HC}$, and $\frac{3}{BC} = \frac{1}{BH}$.

Hence,

$HC + BH = \frac{BC}{2}+ \frac{BC}{3} = \frac{5}{6}BC \neq BC.$ (???)