Cell division is triggered when cells reach a certain size because

This isn't true. There are numerous factors as to when and why a cell divides; just a little bit of searching will return a great deal of information concerning the why and when.
This is true, but isn't the primary reason that a cell divides; I misinterpreted the question.
Growth and cell size does determine when cell division takes place. In short, the demands of the cell become to great for the DNA contained in the cell. Remember, the DNA contains the genetic code to produce the proteome that is needed to maintain the inter-workings of a cell. When the cell becomes to large, the proteome is not able to meet the requirements of the cell, which leads to division.

The link that I included in the source has a great deal of information concerning this.