The volume of a rectangular prism is given by the formula:
Volume = Length * Width * Height
We are given that:
Volume = 48x² + 12x,
Length = 6x,
Width = 2.
We have to find the Height. We know from the formula of volume that:
Height = Volume / (Length * Width)
Substituting the given values, we get:
Height = (48x² + 12x) / (6x * 2)
This simplifies to:
Height = (48x² + 12x) / (12x)
Thus, based on the given conditions, the height of the rectangular prism is represented by the quotient (48x² + 12x) / (12x).