What does "look" mean in the phrase "you don't look your age"? [closed]

I am not a native English speaker. I don't quite understand why the phrase is "you don't look your age" instead of "you don't look like your age" or "you don't look like you are at your age."

I understand that "you don't look your age" means you look younger than people at your age. Just I don't understand how come the meaning of "look" is different from its usual meaning which is to stare / gaze / watch something.

This looks an interesting question.

look = to appear or seem:

You look well! The roads look very icy. That dress looks nice on you. He has started to look his age (= appear as old as he really is).

Cambridge dictionary

And therefore the answer depends on an associated meaning of look, derived from the one you already know, in the following way. "I look at the house"; "the house looks old". "I look at the book; the book looks interesting".