Move the display, watch the wall change. Screen width, bar length, and the seating distance the room actually wants — drawn to scale, because a number on a spec sheet has never once settled an argument with a designer.
A display's advertised size is its diagonal. For a 16:9 panel, the width is the diagonal times 0.8716 and the height is the diagonal times 0.4903 — straight from the aspect ratio. For 21:9 it's 0.9191 and 0.3939.
Seating distance comes from viewing angle. A 40-degree horizontal field — the cinematic end, what THX points at — puts you at about 1.37 times the screen width. A 30-degree field, the SMPTE recommendation and the more forgiving number for a family room, puts you at about 1.87 times the width.