Final answer:
To find the missing side length x of the smaller square after dilation with a scale factor of 1:4, set up a proportion 1:4 = x:8 and solve for x, which will be 2 inches.
Step-by-step explanation:
The question asks how to find the missing side length, x, of the smaller square after a square underwent a dilation with a scale factor of 1:4. To solve this, you can set up a proportion using the information that the side length of the larger square is 8 inches, following the dilation by a factor of 2 from the original side length. The proportion is 1:4 = x:8. By cross-multiplying, you get 4x = 8, which simplifies to x = 2 inches, giving you the side length of the smaller square.