"This table has a height of 1 meter" or "this table has the height of 1 meter"?

Solution 1:

The first sentence is certainly correct and more conventional. The second sentence seems wrong. Consider:

This structure has the length of a long tractor trailer and the height of a large oak.

Here, "the" has the effect of comparing the length (height) in question to the length (height) of a definite or specified object.

According to this reasoning, your second sentence refers to "the width of 16 meters." What is the width of "16 meters"? "16 meters" in itself does not have a width.

To turn matters around, consider this:

This structure has a length of a long tractor trailer and a height of a large oak.

In this case, "a length of" begs for a definite or specified length, such as "16 meters." "A long tractor trailer" is not a length. You could say, "a length of the length of a long tractor trailer," but why would you want to do that? :-)

For a discussion of definite ("the") and indefinite ("a", "an") articles, see https://en.wikipedia.org/wiki/Article_(grammar).

Solution 2:

The first version is more conventional.

But to make the sentence even simpler and more readable, you can simply say:

The structure is 16 meters wide and 30 meters tall.

Solution 3:

The second form is wrong. In that form, you'd say "a width of".

Try another example:-

A cat has a nose. (Correct)

A cat has the nose. (Incorrect)

More than one width (or nose) exists in the universe, so they have "a" width or nose.

However it is normal to say

The width of the structure is 16 metres.

The nose of the cat is black.

In this case you're talking about that one width (or nose) possessed by the structure (or cat), so saying "the" width or nose is OK because the structure (or cat) only has one of them.