Final answer:
If the original rectangle ABCD has a side AD of 2 units, then after a dilation with a scale factor of 3, the length of A'D' would be 6 units. The provided options do not include this answer, so there may be a typo or additional context needed.
Step-by-step explanation:
The question pertains to the concept of dilations in geometry, which is a type of transformation that enlarges or reduces a figure by a scale factor. When you apply a dilation to a figure, every length in the original figure is multiplied by the scale factor to get the corresponding length in the image. As such, to determine the length of side A'D' in rectangle A'B'C'D' after dilation, you multiply the original length of AD in rectangle ABCD by the scale factor.
If the original length of AD is not explicitly given, we cannot determine the exact length of A'D' after the dilation. However, based on the question's structure, it appears that the original length of AD could be 2 units, as a dilation using a scale factor of 3 would then give us
A'D' = AD × scale factor
A'D' = 2 units × 3
A'D' = 6 units
This result is not in the provided options, suggesting a possible typo in the question or choices. In instances like this, it's important to refer back to the original problem or seek additional clarification.