A model of a house was built using the scale 5 in:25 ft. If a window in the model is 1.5 in. wide, how wide is the actual window?
Understand the Problem
The question is asking to determine the actual width of a window based on a scale model. The scale is given as 5 inches in the model corresponds to 25 feet in reality. The width of the window in the model is 1.5 inches, and we need to calculate how wide that would be in the actual size.
Answer
The actual width of the window is $7.5 \, \text{ft}$.
Answer for screen readers
The actual width of the window is $7.5 , \text{ft}$.
Steps to Solve
- Understand the scale of the model
The model's scale is given as 5 inches corresponds to 25 feet. This means that every 5 inches on the model represents 25 feet in reality.
- Find the conversion factor
We need to establish the conversion ratio from the model dimensions to real dimensions.
The conversion is calculated as follows: $$ \text{Scale factor} = \frac{25, \text{ft}}{5, \text{in}} = 5 , \text{ft/in} $$
- Calculate the actual width of the window
Now that we know the conversion factor, we can calculate the actual width of the window.
Given that the width of the window in the model is 1.5 inches, we can determine the actual width using the formula: $$ \text{Actual width} = \text{Model width} \times \text{Scale factor} = 1.5, \text{in} \times 5, \text{ft/in} $$
- Calculate the result
Perform the multiplication: $$ \text{Actual width} = 1.5 , \text{in} \times 5 , \text{ft/in} = 7.5 , \text{ft} $$
The actual width of the window is $7.5 , \text{ft}$.
More Information
This calculation illustrates how to use scale models to determine real-world dimensions. A scale factor allows us to convert measurements easily from models to actual sizes.
Tips
- Confusing the units of measurement, such as not converting inches to feet when necessary.
- Not applying the scale correctly; ensure you multiply by the correct conversion factor.
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