In this case it indicates a length, so the singular form is used in Dutch. The plural is only used if the meters are seen as separate entities: de weg heeft drie meters/stukken met veel gaten (the road has three meters/pieces with lots of holes). As you can see by the type of sentence, this usage is not that common (it's more common for length in time uren, jaren which follow the same principle).
Also meter is used in the meaning measurement device, clearly this are separate entities, so the plural form is used if there are more than one, e.g. Ik heb twee thermometers.
Did anyone else hear "meter lang" as sounding almost exactly like "Nederland?"
I would expect this to be accepted, am I wrong? "The tail is five meters tall"