This structure has a width of 16 meters and a height of 30 meters.
or
This structure has the width of 16 meters and the height of 30 meters.
Considering the fact that every object has one of the dimensions of width and height, can we use the definite article as in the second example sentence? Which is more conventional?
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).
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.
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.
The second form would be appropriate only in cases where there was an earlier reference to a "height of one meter", and would likely come across as stilted even then, e.g. "The dog will need to practice jumping with objects at heights of 1.0m, 1.5m, and 2.0m, depending upon desired classification. This table has the height of 1.0m."
Situations involving "the" with a measurement are much more common if there is an additional adjectival phrase qualifying the measurement, e.g. "This hammer has the 5kg mass necessary to drive ACME nails," or "This device has the short 2cm height needed for it to fit below the shelf." Even those, however, could often be improved as e.g. "The 5kg mass of this hammer is sufficient to drive ACME nails", or "The 2cm height of this device is short enough to let it fit below the shelf."
'a width' and a 'length' would be considered correct usage in England and in any case metres (meters) may well become as odd as Rods, Poles etc. in linear measurement. 'Correct' use of the English language was set out in Fowler H.G OUP 1906 , Clarendon Press, Oxford. But that work has lost favour even in Oxford.
