Rihanna planned a rectangular courtyard for a park and made a scale drawing using inches as the unit of measurement. she originally planned for the length of the actual courtyard to be 54 feet, but she decided to change it to 72 feet. if the length of the courtyard is 18 inches in her scale drawing, which statement about the change of scale is true?

a one inch represented 1 foot in the first scale, but now 1 inch represents 4 feet in the second scale.
b one inch represented 4 feet in the first scale, but now 1 inch represents 3 feet in the second scale.
c one inch represented 54 feet in the first scale, but now 1 inch represents 72 feet in the second scale.
d one inch represented 3 feet in the first scale, but now 1 inch now represents 4 feet in the second scale.

Hey there!

We can utilize division and fractions to find the original scale and the new scale of this situation. 

For the original scale:

, meaning that for every 18 inches on the map, the length of the courtyard would measure 54 feet

We can divide this fraction by a greatest common factor of 18 to get it to:

, meaning that for every 1 inch on the map, the length of the courtyard would measure 3 feet

For the new scale:

, meaning that for every 18 inches on the map, the length of the courtyard would measure 72 feet

We could also divide this fraction by a greatest common factor of 18 to get it to:

, meaning that for every 1 inch on the map, the length of the courtyard would measure 4 feet

So, the scale went from  to , or from 3 feet in the first scale to 4 feet in the second scale. 

Your answer will be D. 

Hope this helped you out! :-)

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