Final answer:
The area of a square dilated by a scale factor of 3.5 is 12.25 times greater than the original. The perimeter is only 3.5 times longer, not seven. Thus, the correct statement is the one regarding the area of the dilated square compared to the original.
Step-by-step explanation:
If a square is dilated by a scale factor of 3.5, we need to consider the effects on both the perimeter and the area of the square. When a two-dimensional shape like a square is dilated, the lengths of the sides are multiplied by the scale factor. Therefore, if the original square had sides of length 's', the dilated square will have sides of length '3.5s'.
For the perimeter, since a square has four equal sides, the perimeter of the original square is '4s'. After dilation, the perimeter of the square becomes '4(3.5s)' which simplifies to '14s'. This means that the perimeter of the dilated square is 3.5 times longer than that of the original square, not seven times longer.
For the area, since the area of a square is given by 'side length squared' (s^2), the area of the original square is 's^2'. After dilation, the area of the square becomes '(3.5s)^2' which is '12.25s^2'. This shows that the area of the dilated square is 12.25 times larger than the area of the original square because the scale factor for the area is the square of the linear scale factor (3.5^2).
Therefore, the true statement about the dilation is that the area of the dilated square is 12.25 times greater than the area of the original square.