Not a trick question by any means.
I assume you mean either its width or height - rather then front-to-back measurements.
Bezel sizes do indeed vary and some vendor and manufacturer websites let you compare TVs or filter results by their dimensions.
He asks for width. The screen is 35" wide. The edges must be at least 1" wide. So, "smallest width" is about 37".
Now, over to 40" TV owners to measure theirs and we'll find out which is the "smallest width 40" TV".