Final answer:
An equivalent scale to 1:96, 1 inch to 8 feet, and 1/8 inch to 1 foot is 1/4 inch to 2 feet. By comparing the model size to the actual size and using unit conversions, we can determine that these scales are proportional to one another.
Step-by-step explanation:
Another scale that is equivalent to 1 to 96 (1 inch to 8 feet) and 1/8 inch to 1 foot can be expressed as 1/4 inch to 2 feet. Each of these scales indicates that the scale model or drawing is smaller than the actual object by the same proportion. To figure out the scale factor for these scales, divide the model or drawing measurement by the real-life measurement to get the ratio that represents the scale factor.
- Scale 1:1/4 inch to 2 feet (1:48)
- Scale 2:1/2 inch to 4 feet (1:96)
- Scale 3:1 inch to 8 feet (1:96)
For example, converting the 1 inch to 8 feet scale to the new scale, we use the fact that there are 12 inches in a foot and divide 8 feet into inches (8 x 12 = 96 inches). Then we have 1 inch representing 96 inches in real life, which is the same as saying 1/4 inch represents 2 feet because 2 feet is 24 inches, and 24 is 1/4 of 96. So, 1/4 inch on the scale model represents 2 feet in real life, which is an equivalent scale to the others provided.