Answer:
The actual dimensions of the room are 1/32 by 23/608 units
Step-by-step explanation:
To find the actual dimensions of the room from the scaled drawing, you can use the scale factor provided. In this case, the scale is 76:1, which means that for every 76 units on the drawing, it represents 1 unit in actual size.
Now, you have the dimensions on the drawing: 2 3/8 by 2 7/8. To find the actual dimensions, you'll need to divide these values by the scale factor (76). Let's start by converting the mixed numbers to improper fractions:
2 3/8 = (2 * 8 + 3)/8 = 19/8
2 7/8 = (2 * 8 + 7)/8 = 23/8
Now, divide each dimension by the scale factor:
Actual Length = (19/8) / 76
Actual Width = (23/8) / 76
To simplify, you can also multiply by the reciprocal of 76, which is 1/76:
Actual Length = (19/8) * (1/76)
Actual Width = (23/8) * (1/76)
Now, calculate these values:
Actual Length = (19/8) * (1/76) = 19/608
Actual Width = (23/8) * (1/76) = 23/608
Now, let's simplify the fractions:
Actual Length = 19/608 = 1/32
Actual Width = 23/608 = 23/608
So, the actual dimensions of the room are 1/32 by 23/608 units. These dimensions are in the same units as the scale, which is 76:1. If you need to express them in a specific unit of measurement (e.g., feet, meters), you'll need to know the unit of measurement used in the scale, and you can convert accordingly.