An architect

An architect makes a model of a new house. The model shows a tile patio in the backyard. In the model each tile has length of 1/2 inch and width of 1/6 inch. The actual tiles have length of 2/3 feet and width 2/9 feet. What is the ratio of the length of a tile in the model to the length of the actual tile? What is the ratio of the area of a tile in the model to the area of an actual tile?

Correct result:

k1 =  1:16
k2 =  1:288


a=1/2=12=0.5 inch b=1/6=160.1667 inch  a2=2/3=230.6667 ft b2=2/8=14=0.25 ft  x=a2 inch=a2 12  inch=0.6667 12  inch=8 inch y=b2 inch=b2 12  inch=0.25 12  inch=3 inch  k1=a/x=0.5/8=116=0.0625=1:16   Verifying Solution:  K1=b/y=0.1667/3=1180.0556 K1k1
S1=a b=0.5 0.1667=1120.0833 inch2 S2=x y=8 3=24 inch2  k2=S1/S2=0.0833/24=12880.0035=1:288

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