Final answer:
The side lengths of the image after a square with an area of 25 is dilated by a scale factor of 6 would be 30 inches.
Step-by-step explanation:
If a square with an area of 25 is dilated by a scale factor of 6, we first need to find the side length of the original square. Since the area is 25, the side length of the original square is the square root of 25, which is 5. When we apply the scale factor of 6 to this side length, we multiply the original side length by the scale factor.
The side length of the image would be:
Original side length x Scale factor = 5 x 6 = 30.
Therefore, the side lengths of the image would be 30 inches.