Question 214724
A sofa is 6 feet long. In a scale drawing, the sofa is 3 inches long. Find the scale of the drawing without units.


Given the sofa is 6 feet long, the scale drawing 3 inches long.  Let s be the scale ratio without units.  Note 1 foot = 12 inches then 1/4 feet is 3 inches.


I'll give two scale factors depending how you want the answer.


APPROACH 1.  Hence, s=6/3 or s=1/2.  This means at if the length is 3 feet then the scale drawing is 3*(1/2)=1.5 inches.


So this is a scale conversion of feet/inches (so this is not unitless)


APPROACH 2.  We can change the scale factor by changing the denominator to 1/4=3 inches.  So


s=6/(1/4)=24.  So the scaling is 24 to 1.  So 6 feet/24= 1/4 feet or 3 inches in the scale drawing.  So this is unitless scale s since the conversion is feet/feet.


I hope the above steps were helpful. 


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And good luck in your studies!


Respectfully,
Dr J