If model shows the width of a tile is 1/6 in. And the actual tile has a width of 2/9 ft. What is the ratio of a tile in the model to the area of an actual tile?

1/256

Step-by-step explanation:

The ratio of linear dimensions of the tile is ...

model : tile = (1/6 in) : (2/9 ft) · (12 in/ft) = 1/6 : 24/9

= (1/6) (9/24) = 9/144 = 1/16

Then the ratio of area dimensions is ...

model area : tile area = (model : tile) ² = (1/16) ²

model area : tile area = 1/256