Minimal dimension of BG (Ex)

Let $G$$<wikitex>; Let $G$ and $G'$ be torsionfree hyperbolic groups. Show that the minimal dimension of finite $CW$-complex models for $BG$ and $BG'$ agree if $G$ and $G'$ are quasi-isometric. Is the converse true? </wikitex> [[Category:Exercises]] [[Category:Exercises without solution]]G$ and $G'$$G'$ be torsionfree hyperbolic groups. Show that the minimal dimension of finite $CW$$CW$-complex models for $BG$$BG$ and $BG'$$BG'$ agree if $G$$G$ and $G'$$G'$ are quasi-isometric. Is the converse true?