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1 vote
1 vote
A new medical complex being built has a rectangular base. It is 300 ft long, 120 ft wide, and 50 ft tall. If the architect's scale model is 36 in. long, what are the width and height of the model?

A. 14.4 in. wide, 6 in. tall
B. 7.2 in. wide, 3 in. tall
C. 86.4 in. wide, 36 in. tall
D. 36 in. wide, 15 in. tall

User Derwiwie
by
2.9k points

2 Answers

23 votes
23 votes

Final answer:

To find the width and height of the model, the scale factor based on the given lengths is determined and then used to convert the actual dimensions to model dimensions. The model width is found to be 14.4 inches, and the height is 6 inches, which corresponds to option A.

Step-by-step explanation:

To determine the width and height of the model for the medical complex, we first need to understand the scale used by the architect. We're given that the actual building is 300 ft long and the model is 36 inches long. Based on this information, we can establish the scale factor:

  • 300 ft (actual length) = 36 in (model length)

The scale factor would be 300 ft / 36 in. To convert feet to inches (since the model measurements are in inches), we multiply by 12 inches/1 foot:

Scale factor = (300 ft * 12 in/1 ft) / 36 in = 100

Now, we apply this scale factor to find the width and height of the model:

  • Width of the actual building = 120 ft
  • Height of the actual building = 50 ft

To find the dimensions in the model:

  • Width of the model = Width of actual building / Scale factor = (120 ft * 12 in/1 ft) / 100 = 14.4 in
  • Height of the model = Height of the actual building / Scale factor = (50 ft * 12 in/1 ft) / 100 = 6 in

The width and height of the model are therefore 14.4 inches wide and 6 inches tall, which corresponds to option A.

User Earid
by
2.5k points
24 votes
24 votes

Answer:

14.4 inches wide, 6 inches tall

Step-by-step explanation:

User Avivit
by
2.6k points