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 model length to inches: $1\ \text{ft} = 12\ \text{inches}$.
Scale factor: $\frac{\text{Actual length}}{\text{Model length}} = \frac{50\ \text{ft}}{12\ \text{inches}} = \frac{25}{6}\ \text{ft/inch}$

Step2: Calculate actual window height (Q14)

Convert model window height to improper fraction: $1\frac{1}{5} = \frac{6}{5}\ \text{inches}$
Actual height: $\frac{25}{6} \times \frac{6}{5} = 5\ \text{ft}$

Step3: Find unit scale factor (Q15)

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

Step4: Calculate actual length (Q15)

$\text{Actual length} = 1.6 \times 31.25 = 50\ \text{ft}$

Step5: Calculate actual width (Q15)

$\text{Actual width} = 2.8 \times 31.25 = 87.5\ \text{ft}$

Step6: Calculate actual height (Q15)

$\text{Actual height} = 11.2 \times 31.25 = 350\ \text{ft}$

Answer:

1. $5$ feet
2. Length: $50$ feet, Width: $87.5$ feet, Height: $350$ feet