Tính chu vi của tam giác ABC

$$\begin{gathered} \mathrm{Cho} ∆\mathrm{ABC} \mathrm{vuông} \mathrm{tai} \mathrm{A}. \mathrm{Các} \mathrm{tia} \mathrm{phân} \mathrm{giác} \mathrm{của} \mathrm{góc} \mathrm{B}\hspace{0.17em}\mathrm{và} \mathrm{Ccắt} \mathrm{nhau} \mathrm{ở} \mathrm{I}.\mathrm{Kẻ} \mathrm{IH} \mathrm{vuông} \mathrm{góc} \mathrm{với} \mathrm{BC} \left(\mathrm{H}\in \mathrm{BC}\right). \\ \mathrm{Biết} \mathrm{HI}=1\mathrm{cm}, \mathrm{HB}=2\mathrm{cm},\mathrm{HC}=3\mathrm{cm}. \mathrm{Tính} \mathrm{chu} \mathrm{vi} \mathrm{tam} \mathrm{giác} \mathrm{ABC} \end{gathered}$$