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Distance metrics and their extensions are widely accepted tools in supporting distance-based decision making, consensus building, and preference aggregation systems. For several models of this nature, it may be necessary to elucidate the problem output in the original input domain. When a particular parameter of interest is desired to be produced in this original domain, i.e., the <i>scale</i>, the decision makers simply resort to constraints that function in parallel with this goal. However, there exist some cases where such a membership is guaranteed by the mathematical properties of the distance metric utilized. In this paper, we argue that the <i>scale constraints</i> utilized in this manner under the distance-metric optimization framework are, in some cases, completely redundant. We provide necessary mathematical proofs and illustrate our arguments through an abstract physical system, examples, a case study, and a brief computational experiment.