Final answer:
The area of the largest face of a block will increase by a factor of four if the block's dimensions are each doubled. This is because area is a function of two dimensions, and doubling both dimensions multiplies the area by four.
Step-by-step explanation:
The question is asking how the area of the largest face of a block would change if its dimensions, length, width, and height, were each doubled. The area of a rectangle is calculated by multiplying its length by its width. If you consider the block's face as a rectangle and double both the length and the width, the new area will be the original length multiplied by 2 and the original width multiplied by 2. So, the new area is L x 2 multiplied by W x 2, which simplifies to 4 times the original area (LW).
For instance, Block A has a face with area L x 2L, resulting in 2L². If you double each dimension to get Block B, the largest face would be 2L x 4L, or 8L². The factor change in area from Block A to Block B is by a factor of four (2L² x 4 = 8L²).
Therefore, the correct answer for Marta's larger square compared to her smaller square is that the area increases by a factor of four.