Final answer:
The correct dimensions of the art shed, calculated by scaling up the blueprint dimensions of 1 ½ inches by 32 inches by the scale factor of 40:1, are 5 feet by 106 feet 8 inches, which shows a discrepancy in the multiple-choice options provided.
Step-by-step explanation:
Naoko is building a small art shed in the backyard and has created a blueprint with a scale ratio of 40:1. According to the blueprint, the dimensions of the art space are 1 ½ inches by 32 inches. To find the actual dimensions of the art shed in feet, we first convert the blueprint measurements to actual size by multiplying each dimension by the scale factor.
1 ½ inches multiplied by 40 equals 60 inches. Since there are 12 inches in a foot, this is equivalent to 5 feet. For the width, 32 inches multiplied by 40 equals 1280 inches, which when divided by 12 inches per foot, gives us 106 ⅔ feet or 106 feet 8 inches. Therefore, the actual dimensions of the art shed are 5 feet by 106 feet 8 inches, which is not listed as an option in the multiple-choice question, indicating there might be a mistake in the provided choices.