Tim wants to model a dollhouse from a real house that measures 60 feet in length by 28 feet in width. He decides to use a scale in which [tex]$1 / 4$[/tex] inch equals 1 foot. What will the dimensions of his model be?
Length = $\square$ inches
Width = $\square$ inches
Answer (2)
The problem provides the dimensions of a real house and a scale factor for a dollhouse model.
The length of the dollhouse model is found by multiplying the real house length by the scale factor: 60 × 4 1 = 15 inches.
The width of the dollhouse model is found by multiplying the real house width by the scale factor: 28 × 4 1 = 7 inches.
The dimensions of the dollhouse model are 15 inches in length and 7 inches in width.
Explanation
Understanding the Problem Tim is building a dollhouse model of a real house. The real house has a length of 60 feet and a width of 28 feet. Tim is using a scale where 4 1 inch on the model represents 1 foot on the real house. We need to find the length and width of the dollhouse model in inches.
Calculating the Length To find the length of the dollhouse model, we need to multiply the actual length of the house by the scale factor. The actual length is 60 feet, and the scale factor is 4 1 inch per foot. So, the length of the model in inches is: Length = 60 feet × 4 1 foot inch
Finding the Length Now, we perform the multiplication: Length = 60 × 4 1 = 15 inches So, the length of the dollhouse model is 15 inches.
Calculating the Width To find the width of the dollhouse model, we do the same thing, but with the actual width of the house. The actual width is 28 feet, and the scale is still 4 1 inch per foot. So, the width of the model in inches is: Width = 28 feet × 4 1 foot inch
Finding the Width Now, we perform the multiplication: Width = 28 × 4 1 = 7 inches So, the width of the dollhouse model is 7 inches.
Stating the Answer Therefore, the dimensions of Tim's dollhouse model will be 15 inches in length and 7 inches in width.
Length = 15 inches Width = 7 inches
Examples
Scale models are used in various fields, such as architecture and engineering, to represent real-world objects or structures. For example, architects create scale models of buildings to visualize the design and present it to clients. Similarly, engineers use scale models of bridges or airplanes to test their designs in a wind tunnel. Understanding scale and proportions is crucial in these applications to ensure the model accurately represents the real object.
Tim's dollhouse model will have a length of 15 inches and a width of 7 inches. These dimensions are obtained by scaling down the actual house measurements using a scale of 4 1 inch per foot. The calculations involve multiplying the actual dimensions by the scale factor.
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