Final answer:
The perimeter of the new hexagon will be one and one-third times larger than the original hexagon's perimeter, since it is scaled by 4/3.
Step-by-step explanation:
When a regular hexagon is dilated by a scale factor of 4/3, the new hexagon's perimeter will also be scaled by that same factor. If the original hexagon had a perimeter 'P', then the new hexagon will have a perimeter of (4/3)P.
To apply this concept with an example, let's assume we have a square with a side length of 4 inches.
If we have a similar square with dimensions twice of the first one, its side length will be 8 inches (4 inches x 2).
The area of shapes scales by the square of the scale factor, so the area of the larger square will be 4 times larger than the area of the smaller square since the scale factor is 2, and 2 squared equals 4.
Therefore, the perimeter of the new hexagon compared with the original will be one and one-third times larger.