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 one half in.
and width one sixth in.
The actual tiles have length two thirds ft
and width two ninths 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.
Answers
Ratio of Sides = 1/16 & Ratio of Area = 1/256
Step-by-step explanation:
In the model, each tile has length 1/2 inch and width 1/6 inch
The actual tiles have length 2/3 ft & width 2/9 ft
1 ft = 12 inch
=> 2/3 ft = 8 inch
2/9 ft = 8/3 inch
ratio of the length of a tile in the model to the length of an actual tile
= (1/2)/ (8)
= 1/16
or Ratio of Width = Ratio of length = (1/6)/(8/3) = 3/48 = 1/16
Ratio of Area = (1/16)² = 1/256
or Area of tile in model = (1/2)(1/6) = 1/12 inch²
Area of tile in actual = 8 * 8/3 = 64/3 inch²
Ratio of Area = (1/12) / (64/3) = 1/256
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