Final answer:
Ai's model window is a scale representation of the actual window because the ratios of the model's dimensions to the actual dimensions are equal, with both simplifying to 1:54.
Step-by-step explanation:
To determine if Ai's model treehouse window is an accurate representation of the actual window, we must compare the ratios of the heights and the widths from the model to their corresponding actual dimensions. The model window has a height of 1/3 inch and a width of 1/6 inch. The actual window is 1/2 yard (18 inches) tall and 1/4 yard (9 inches) wide.
Converting the actual dimensions to inches for easier comparison: 1/2 yard = 18 inches; 1/4 yard = 9 inches. Now we check the ratios: Model height to actual height is 1/3 inch : 18 inches and model width to actual width is 1/6 inch : 9 inches. If the ratios are equal, the model is a scale representation.
The height ratio simplifies to 1:54, and the width ratio simplifies to 1:54. Since both ratios are equal, Ai's model window is indeed a scale representation of the actual window.