Answer:
a) ![\frac{8 \,ft}{reduced\,drawing} =\frac{1\,ft}{3/8\,in}](https://tex.z-dn.net/?f=%5Cfrac%7B8%20%5C%2Cft%7D%7Breduced%5C%2Cdrawing%7D%20%3D%5Cfrac%7B1%5C%2Cft%7D%7B3%2F8%5C%2Cin%7D)
b) Reduced drawing size = 3 in
c) ![\frac{actual\,size}{6.75\,in} =\frac{1\,ft}{3/8\,in}](https://tex.z-dn.net/?f=%5Cfrac%7Bactual%5C%2Csize%7D%7B6.75%5C%2Cin%7D%20%3D%5Cfrac%7B1%5C%2Cft%7D%7B3%2F8%5C%2Cin%7D)
d) actual length of the room: 18 ft
Step-by-step explanation:
The proportion that CAD creates is given by:
![\frac{actual\,size}{reduced\,drawing} =\frac{1\,ft}{3/8\,in}](https://tex.z-dn.net/?f=%5Cfrac%7Bactual%5C%2Csize%7D%7Breduced%5C%2Cdrawing%7D%20%3D%5Cfrac%7B1%5C%2Cft%7D%7B3%2F8%5C%2Cin%7D)
Then:
a) if a wall is 8 ft tall, the proportion gives:
![\frac{actual\,size}{reduced\,drawing} =\frac{1\,ft}{3/8\,in}\\\frac{8\,ft}{reduced\,drawing} =\frac{1\,ft}{3/8\,in}](https://tex.z-dn.net/?f=%5Cfrac%7Bactual%5C%2Csize%7D%7Breduced%5C%2Cdrawing%7D%20%3D%5Cfrac%7B1%5C%2Cft%7D%7B3%2F8%5C%2Cin%7D%5C%5C%5Cfrac%7B8%5C%2Cft%7D%7Breduced%5C%2Cdrawing%7D%20%3D%5Cfrac%7B1%5C%2Cft%7D%7B3%2F8%5C%2Cin%7D)
b) to solve this proportion for the reduced drawing size, we cross multiply and then isolate the unknown on one side by dividing both sides by "1 ft":
![\frac{8\,ft}{reduced\,drawing} =\frac{1\,ft}{3/8\,in}\\3/8\, in \,*\,8\,ft=reduced\,drawing\,*\,1\,ft\\reduced\,drawing=\frac{3/8\,in\,*\,8\,ft}{1\,ft}\\reduced\,drawing=3 \,in](https://tex.z-dn.net/?f=%5Cfrac%7B8%5C%2Cft%7D%7Breduced%5C%2Cdrawing%7D%20%3D%5Cfrac%7B1%5C%2Cft%7D%7B3%2F8%5C%2Cin%7D%5C%5C3%2F8%5C%2C%20in%20%5C%2C%2A%5C%2C8%5C%2Cft%3Dreduced%5C%2Cdrawing%5C%2C%2A%5C%2C1%5C%2Cft%5C%5Creduced%5C%2Cdrawing%3D%5Cfrac%7B3%2F8%5C%2Cin%5C%2C%2A%5C%2C8%5C%2Cft%7D%7B1%5C%2Cft%7D%5C%5Creduced%5C%2Cdrawing%3D3%20%5C%2Cin)
c) If the drawing shows a room with length 6.75 in, we use the proportion equation again, replacing now the "<em>reduced drawing</em>" quantity with 6.75 in, and getting ready to solve for the unknown "<em>actual size</em>":
![\frac{actual\,size}{reduced\,drawing} =\frac{1\,ft}{3/8\,in}\\\frac{actual\,size}{6.75\,in} =\frac{1\,ft}{3/8\,in}](https://tex.z-dn.net/?f=%5Cfrac%7Bactual%5C%2Csize%7D%7Breduced%5C%2Cdrawing%7D%20%3D%5Cfrac%7B1%5C%2Cft%7D%7B3%2F8%5C%2Cin%7D%5C%5C%5Cfrac%7Bactual%5C%2Csize%7D%7B6.75%5C%2Cin%7D%20%3D%5Cfrac%7B1%5C%2Cft%7D%7B3%2F8%5C%2Cin%7D)
d) To solve for the unknown, since it is already in the numerator, we just need to multiply both sides of the equal sign by 6.75 in:
![\frac{actual\,size}{6.75\,in} =\frac{1\,ft}{3/8\,in}\\actual\,size= \frac{1\,ft\,*6.75\,in}{3/8\,in} \\actual\,size=18\,ft](https://tex.z-dn.net/?f=%5Cfrac%7Bactual%5C%2Csize%7D%7B6.75%5C%2Cin%7D%20%3D%5Cfrac%7B1%5C%2Cft%7D%7B3%2F8%5C%2Cin%7D%5C%5Cactual%5C%2Csize%3D%20%5Cfrac%7B1%5C%2Cft%5C%2C%2A6.75%5C%2Cin%7D%7B3%2F8%5C%2Cin%7D%20%5C%5Cactual%5C%2Csize%3D18%5C%2Cft)