SOLUTION: 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 two thirds in. 2 3 in. and width one third in.

Question 1019594: 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 two thirds in.
2
3 in. and width one third in.
1
3 in. The actual tiles have length three fourths ft
3
4 ft and width three eighths ft
3
8 ft. What is the ratio of the length of a tile in the model to the length of an actual tile? What is the ratio of the area of a tile in the model to the area of an actual tile? Use pencil and paper. Describe two ways to find each ratio.
Find the ratio of the length of the tile in the model to the length of the actual tile. First multiply to find the length of an actual tile in inches.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The length, in inches, of a tile in the model is .
The length, in inches, of an actual tile is .
Multiplying , the length of an actual tile in feet, by AMP Parsing Error of [(12inches/"1 foot"]: Invalid expression. Closing bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 187. . gives the length in inches,
and that is probably what the teacher meant by "irst multiply to find the length of an actual tile in inches."

The ratio of the length of a tile in the model to the length of an actual tile is
.

Since we need "two ways to find each ratio",
we need to think of what the teacher's idea could be of a different way to calculate the above ratio.
Calculating both lengths in another unit first would be another way,
but using feet as a unit makes the calculation more complicated,
and using centimeters, or millimeters makes the pencil and paper arithmetic too nasty for my taste.
How about using thirds of an inch as a unit?
That makes the calculations easy.
The length, in thirds of an inch, of a tile in the model is .
The length, in thirds of an inch, of an actual tile is .
The ratio of the length of a tile in the model to the length of an actual tile is
.

We could calculate the ratio of the width of a tile in the model to the width of an actual tile,
but that ratio should be the same in a model,
and we should be able to trust the architect's calculations and model-making accuracy.

When the dimensions of similar 2-D figures are in the ratio ,
the ratios of their surface areas are in the ratio .
So, the ratio of the area of a tile in the model to the area of an actual tile is
.
Since we need "two ways to find each ratio",
we need to think of what the teacher's idea could be of a different way to calculate the above ratio.
It will be an unnecessarily complicated way,
calculating the area of a tile in the model, and the area of an actual tile.
To make calculation easier, we could use thirds of an inch as unit of length.
The length, in thirds of an inch, of a tile in the model is .
The width, in thirds of an inch, of a tile in the model is .
The area of a tile in the model (in our chosen unit squared) is .
The length, in thirds of an inch, of an actual tile is , as calculated before.
The width, in thirds of an inch, of an actual tile is .
The area of an actual tile is .
The ratio of the area of a tile in the model to the area of an actual tile is
.
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SOLUTION: An architect makes a model of a new house. The model shows a tile patio in the backyard. In the&#8203; model, each tile has length two thirds in. 2 3 in. and width one third in.

SOLUTION: 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 two thirds in. 2 3 in. and width one third in.