Question

A floor plan has a 72:1 scale. on drawing, on of the rooms measure 3 ft 5/8 by 3 ft 1/2. the actual dimensions would be

a) 216 1/4 ft by 252 ft
b) 228 ft by 252 ft
c) 216 1/4 ft by 245 ft
d) 228 ft by 245 ft

Answer 1

To determine the actual dimensions of a room from a floor plan with a 72:1 scale, the measurements on the plan must be converted to feet, corrected for the scale, and then multiplied by 72. None of the provided answer options match the exact calculations, but the closest would be option (b) 228 ft by 252 ft.

Step-by-step explanation:

The student's question involves finding the actual dimensions of a room based on its scaled measurements provided in a floor plan. The scale given is 72:1, meaning that every unit on the plan represents 72 units in reality. The room on the drawing measures 3 feet and 5/8 inches by 3 feet and 1/2 inches. To find the actual dimensions:

1. Convert the inches into feet (5/8 inch = 0.05208 feet, 1/2 inch = 0.04167 feet).
2. Add these conversions to the respective feet measurements on the plan (3 feet 5/8 inches becomes 3.05208 feet, 3 feet 1/2 inch becomes 3.04167 feet).
3. Multiply these feet measurements by the scale factor (72) to obtain the actual dimensions.

So, the actual length is 3.05208 feet * 72 = 219.75 feet, and the actual width is 3.04167 feet * 72 = 218.99 feet.

As none of the provided answers exactly matches these calculations, it seems there might be a rounding or a mistake in the provided options or the original question might need revisiting. However, the closest provided answer considering the likely roundings would be:

Option (b) 228 ft by 252 ft.