A dollhouse uses a scale factor of \(\frac{1}{12}\). The perimeter of a square room in the dollhouse is 36 inches. What is the length of the full-size room?
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Answer (3)
k= 1/12 perimeter of doll house= 36 inches :. length of doll house= 36inches / 4 = 9 inches length of actual= length of doll house x k(inverse) :. actual lenght= 9 inches x 12/1 = 108 inches
The question asks about converting the perimeter of a room in a dollhouse to the full-size dimensions using a scale factor of 1:12. The given perimeter of the square room in the dollhouse is 36 inches. Since the perimeter is the total distance around the square, we can first find the length of one side of the square room in the dollhouse and then use the scale factor to find the length of the full-size room.
First, divide the total perimeter by 4 to find the length of one side in the dollhouse: 36 inches ÷ 4 = 9 inches.
To find the full size, multiply the length by the scale factor: 9 inches × 12 = 108 inches.
Convert inches to feet (since there are 12 inches in a foot): 108 inches ÷ 12 = 9 feet.
Therefore, the length of the full-size room is 9 feet.
By calculating the side length of the dollhouse room from its perimeter, we find that the side length is 9 inches. Using the scale factor of 1:12, we convert this length to the full size, resulting in 9 feet for the length of the full-size room. Thus, the final answer is 9 feet.
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