Scale factor of office building to the model?

Question

An architect is designing an office building that is to be a width of 50 feet, a length of 50 fee, and a height of 100 feet. A scale model of the same building is to have a width of 18 inches, a length of 18 inches, and a height of 36 inches. What is the scale factor if office building to the model? 

Answer 1

The scale factor of the office building to the model is the ratio of the corresponding distances in the building to those in the model.  The only tricky part is that the measurements have to be in the same units.  So you need to convert inches to feet (or vice versa) using the conversion factor 12 inches = 1 foot.  If we convert the height of the model from 36 inches to 3 feet then we see that the scale factor is 

 

100 : 3

 

or 33 (1/3) : 1

 

You can try converting the width and length to both feet and inches to make sure you get the same answer each time.