Respuesta :
Answer
A) The ratio of the length of a tile in the model to the length of actual tile
1 inch on the model = 9 inches on the actual tile
B) The ratio of the area of a tile in the model to the area of actual tile is
1 square inch on the model = 81 square inches on the actua tile
Explanation
Before we try to solve this, we need to convert both measurements into the same units. It should be noted that
1 ft = 12 inches.
So, for the actual model,
1 ft = 12 inches.
½ ft = ½ (12 inches) = 6 inches
(3/8) ft = (3/8) (12 inches) = 4.5 inches
So, we will now compare corresponding dimensions to write the ratio of length of a tile in the model to the length of the actual tile.
The model has a length of (2/3) in and a width of (1/2) in
The actual tile has a length of 6 inches and a width of 4.5 inches.
(2/3) inches on the model = 6 inches on the actual tile
Multiply both sides by (3/2)
(2/3) × (3/2) = 6 × (3/2)
1 inch on the model = 9 inches on the actual tile
We can use the width to confirm the answer
(1/2) inches on the model = 4.5 inches on the actual tile
Multiply both sides by 2
(1/2) × 2 = 4.5 × (2)
1 inch on the model = 9 inches on the actual tile
To find the ratio of areas, we will simply find the areas of the model tile and the actual tile.
The area of a rectangle = L × W
The model has a length of (2/3) in and a width of (1/2) in
The area of a rectangle = L × W = (2/3) × (1/2) = (1/3) square inches
The actual tile has a length of 6 inches and a width of 4.5 inches.
The area of a rectangle = L × W = 6 × 4.5 = 27 square inches
(1/3) square inches on the model = 27 square inches on the actual tile
Multiply both sides by 3
(1/3) × 3 = 27 × 3
1 square inches = 81 square inches
Hope this Helps!!!
