Height is an attribute: it can be measured using the metric, customary or made-up system. An example of the last one is "X is twice as long as my wife's pet, Fluffy". If you don't know what kind of creature Fluffy is then you know next to nothing about X's length. And, incidentally, Fluffy was named with the same sense of humour (!) as the three headed dog in Harry Potter and the Chamber of Secrets.
Height is a physical characteristic and so is neither customary or metric.
Metric.
It is a customary unit.
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It's both.
In many European countries the metric system IS the customary system!
10 feet and 120 inches
It is a customary unit.
The opposing systems are imperial and metric, not customary. But, meters are metric.
The pound is NOT a metric unit.
It is customary.
It can be more or less. An once (customary) is bigger than a gram (metric) but a pound (customary) is smaller than a kilogram (metric).
Metric.
Metric
Metric.
It is a customary unit.
customary
A "gran" is a German measurement, it is neither customary or metric. A "gram" is a metric unit.