Final answer:
To determine the blueprint length of a room that is actually 30 feet, we use the given scale of 1/2 inch per 4 feet. After setting up the proportion, we find that the room would be represented as 3.75 inches on the blueprint.
Step-by-step explanation:
The question involves using a scale factor to convert actual measurements to their corresponding blueprint measurements. Given that 1/2 inch on the blueprint represents 4 feet in actual length, we need to determine the blueprint length of a room that is 30 feet long in reality.
First, we write the unit scale as a ratio: 1/2 inch per 4 feet. To keep units consistent, we can either convert inches to feet or vice versa. In this case, since we're dealing with blueprint measurements, it's easier to convert the actual size to blueprint size, which uses inches. Therefore, we have the following ratio for the blueprint scale:
Blueprint scale: 1/2 inches / 4 feet
= 1 inches / 8 feet
Next, we use this ratio to find the blueprint measurement for a 30-foot long room. Since 1 inch on the blueprint corresponds to 8 feet in reality, we can set up a proportion:
1 inch / 8 feet = x inches / 30 feet
We solve for x, which represents the length on the blueprint.
x = (30 feet) × (1 inch) / 8 feet
Simplify:
x = 3.75 inches
So, on the blueprint, a room that is actually 30 feet long would be represented as 3.75 inches long.