Question

Architects create drawings to model the buildings that will eventually get built. These drawings are

Answer 1

Answer:

a) $\frac{8 \,ft}{reduced\,drawing} =\frac{1\,ft}{3/8\,in}$

b) Reduced drawing size = 3 in

c) $\frac{actual\,size}{6.75\,in} =\frac{1\,ft}{3/8\,in}$

d) actual length of the room: 18 ft

Step-by-step explanation:

The proportion that CAD creates is given by:

$\frac{actual\,size}{reduced\,drawing} =\frac{1\,ft}{3/8\,in}$

Then:

a) if a wall is 8 ft tall, the proportion gives:

$\frac{actual\,size}{reduced\,drawing} =\frac{1\,ft}{3/8\,in}\\\frac{8\,ft}{reduced\,drawing} =\frac{1\,ft}{3/8\,in}$

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":

$\frac{8\,ft}{reduced\,drawing} =\frac{1\,ft}{3/8\,in}\\3/8\, in \,*\,8\,ft=reduced\,drawing\,*\,1\,ft\\reduced\,drawing=\frac{3/8\,in\,*\,8\,ft}{1\,ft}\\reduced\,drawing=3 \,in$

c) If the drawing shows a room with length 6.75 in, we use the proportion equation again, replacing now the "reduced drawing" quantity with 6.75 in, and getting ready to solve for the unknown "actual size":

$\frac{actual\,size}{reduced\,drawing} =\frac{1\,ft}{3/8\,in}\\\frac{actual\,size}{6.75\,in} =\frac{1\,ft}{3/8\,in}$

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:

$\frac{actual\,size}{6.75\,in} =\frac{1\,ft}{3/8\,in}\\actual\,size= \frac{1\,ft\,*6.75\,in}{3/8\,in} \\actual\,size=18\,ft$