Suppose you use prices and square meters, to cluster apartments. Suppose you also use a simple metric, like:

  distance <- sqrt(d_price*2 + d_area*2)

Without normalizing the units somehow, so that they have a meaningfully similar numeric expression, you are essentially only clustering by price, which is in the tens- or hundreds-of-thousands.

You use very little information about the area, because that is in the hundreds, at most thousands.