Question

1. a scale model of a house is 1 ft long. the actual house is 50 ft long. in the model, the window is $1\frac{1}{5}$ inches tall. how many feet tall is the actual window? 15. a model of a skyscraper is 1.6 inches long, 2.8 inches wide, and 11.2 inches high. the scale factor is 8 inches = 250 feet. what are the actual dimensions of the skyscraper?

Explanation:

Step1: Find scale factor (Q14)

First, convert mixed number: $1\frac{1}{5} = 1.2$ inches.
Set up proportion: $\frac{\text{Model length}}{\text{Actual length}} = \frac{1\ \text{ft}}{50\ \text{ft}} = \frac{1.2\ \text{in}}{x\ \text{ft}}$
Simplify scale: $\frac{1}{50} = \frac{1.2}{x}$

Step2: Solve for x (Q14)

Cross multiply: $x = 1.2 \times 50$
$x = 60$

Step3: Find unit scale (Q15)

Scale: $8\ \text{in} = 250\ \text{ft}$, so 1 in = $\frac{250}{8} = 31.25\ \text{ft}$

Step4: Calculate actual length (Q15)

Length: $1.6 \times 31.25 = 50$

Step5: Calculate actual width (Q15)

Width: $2.8 \times 31.25 = 87.5$

Step6: Calculate actual height (Q15)

Height: $11.2 \times 31.25 = 350$

Answer:

1. 60 feet
2. Length: 50 feet, Width: 87.5 feet, Height: 350 feet