Here's why:
* German pronunciation: The "ü" in "Küche" is pronounced like the "oo" in "book" or "foot." This is a short vowel sound.
* English pronunciation: While "Küche" is a German word, it's often pronounced in English with a long "u" sound (like the "u" in "cute"). This is incorrect and doesn't reflect the original German pronunciation.
Therefore, "Küche" has a short vowel sound when pronounced correctly in German.