length is a variable to determine the length  of
the array. You can use other variable but why? The
majority of us use .length because it is very
descriptive and precisely.

I want to know what length  is from the language syntax point of view, and
subsequently what other similar constructions are possible, not to do the same
thing as length (retrieve the length of the array), but to do other operations
on the array. You say length is a variable. Where is it defined?

Is all you wrote here cited from that book, or just the first paragraph? Anyway,
I was aware of the fact that an array  is condidered to be a first-class Object,
BUT the class  Object doesn't have the property length. That's my point.

Is your third paragraph (that begins with "length" is a property...) also cited
from that book? If so, I will be satisfied with that answer. If not, how do you
know it?

Core Java 2 (Volume I Fundamentals) -

"In Java, arrays  are first-class objects. You are
better off not thinking about how arrays are
implemented in Java - accept them as objects that
exist in and of themselves".

Array is a structure of pre-defined length  provided by
the Java language and it can contain values of the
same type.

"length" is a property provided by the Java language.
At the moment, there are no such properties other than
"length"...