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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.
In some contexts, two of these terms -- length and height -- do also have a specific mathematical meaning. 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.