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Length, when referring to measurement in one dimension (as in the length of a line segment or a or a piece of string), has a specialized meaning. So does height when it is used in conjunction with base.
If height were being measured though, the variables would be continuous as there are an unlimited number of possibilities even if only looking at between 1 and 1.1 meters. It is important to remember that both kinds of variables are so grouped based on the scale used to measure them and what is being measured.