"The clothes on the floor are dirty."
Translation:Vestimenta in pavimento sordida sunt.
It would have to be sordido to match with pavimento in case (along with number [singular] and gender [neutuer]).
Vestimenta in pavimento sordido sunt would be more 'The clothes are on the dirty floor'
Adjectives must match with the noun they modify in case, number, and gender.
exactly as you did: with a relative clause. Latin does not normally use prepositional phrases adjectivally, the way English does, so using a relative clause where the prepositional phrase is adjunct to the verb (vestimenta quae in pavimento iacent sordida sunt), or a participle where the prepositional phrase is adjunct to the verbal idea (vestimenta in pavimento iacentia sordida sunt) would be much more normal.