A preposition does not seem to be the appropriate missing word.
A preposition is a word that connects the object of the preposition to another word in the sentence.
In this sentence, the word "length" would be the object of the missing preposition. We don't have a clue which word we're trying to connect "length" to, the subject "man" or the verb "got". Neither makes much sense. Some examples are:
- The man got for length.
- The man got in length.
- The man got about length.
- The man got with length.
A more appropriate part of speech to fill in the blank may be an adjective, to describe the noun "length". For example:
- The man got some length.
- The man got more length.
- The man got less length.
- The man got enough length.