Are the words tent and tenant related? Let’s find out.

A tent is a portable shelter made of fabric or other material stretched over a supporting framework of poles and usually stabilized or secured to the ground with cords and stakes [source].

It comes from the Middle English tente (tent, abode, dwelling place, pavilion) [source, from the Old French tente (tent, temporary hut or other similar building), from Vulgar Latin *tenta (tent), from tentus (stretched, extended, distended), from tendō (to stretch, distend, extend), from Proto-Italic *tendō (I stretch), from the Proto-Indo-European *ten- (to stretch, extend) [source].

A tenant is one that pays rent to use or occupy land, a building, or other property owned by another; a dweller in a place; an occupant [source].

It comes from the Middle English tenaunt (tenant – one who holds real property from another by feudal obligation or payment of rent) [source], from Anglo-Norman tenaunt (tenant), from Old French tenant (holder, possessor [of land or property], tenant, owner), from tenir (to hold), from Latin teneō (I hold, have, grasp), from Proto-Italic *tenēō (I hold), from the Proto-Indo-European *ten- (to stretch, extend) [source].

So they do come from the same PIE root, via different routes. Other words from the same PIE root include tenor, tone, tonic, tune, sustain and content [source].

Incidentally, in Old English the word for tent was teld, from the Proto-Germanic *teldą (tent, drape), which became teld (tent, castle, fort, hut) in Middle English, and teld (tent, to lodge in a tent, to pitch a tent), and tilt (a canvas covering for carts, boats, etc, tent) in Modern English, although these words are no longer used [source].

Tilt, which means to slope or incline (smth), to slant, to be at an angle, to charge (at sb) with a lance, to joust, etc, comes from different roots. Apparently it came to be associated with jousting as the cloth barrier that separated combantants in a joust is called a tilt [source].