"The price of the kitten is thirty euros."
Translation:La prezo de la katido estas tridek eŭroj.
If I understand correctly: -n ending is indeed used for measures, but not when the measure is the subject of the sentence or the description of the subject (in short, after esti).
So here, la prezo estas tridek eŭroj without -n ending, but with kosti, the sentence would become: la katido kostas tridek eŭrojn.
Edit: Duolingo is full of exceptions such as tiu fadeno estas unu metron longa. So, I really am not sure of what I just wrote!...
You'll note that your "exception" contains an adjective that is being quantified; if someone had said, La longo de tiu fadeno estas unu metro, there would have been no accusative.
"one metre long", "three kilogrammes heavy", "two inches wide" etc. would use accusative in the quantifier.
I've never heard anyone say "This book was ten euros expensive", but if one did say it, I'd expect the accusative in the measure word there as well (dek eŭrojn kosta or something like that perhaps).