- Convert the mixed fraction \(1 \frac{1}{8}\) to the improper fraction \(\frac{9}{8}\).
- Use the given scale of \(1\) inch = \(8\) feet to set up the calculation.
- Multiply the blueprint length by the scale factor: \(\frac{9}{8} \times 8 = 9\).
- The actual length of the wall is \(\boxed{9}\) ft.
Explanation
- Problem Analysis and Data Preparation
We are given a scale on an architect's blueprint where \(1\) inch represents \(8\) feet. We need to determine the actual length of a wall that is represented by a line segment of \(1 \frac{1}{8}\) inches on the blueprint. This problem represents a proportional relationship, where the actual length is directly proportional to the blueprint length.
- Setting Up and Solving the Proportion
To perform the calculation, we first convert the mixed fraction representing the blueprint length into an improper fraction:
\[ 1 \frac{1}{8} = 1 + \frac{1}{8} = \frac{8}{8} + \frac{1}{8} = \frac{9}{8} \text{ inches}. \]
Now, given the scale of \(8\) feet per \(1\) inch, we set up the following proportional relationship to find the actual length \(L\):
\[ \frac{\text{Actual Length}}{\text{Blueprint Length}} = \frac{8 \text{ feet}}{1 \text{ inch}} \]
\[ L = \frac{9}{8} \text{ inches} \times 8 \text{ feet/inch} \]
- Calculating the Final Length
By multiplying the blueprint length by the scale factor, we find the actual length:
\[ L = \frac{9}{8} \times 8 = 9 \text{ feet}. \]
The wall's actual length is \(9\) feet.
Examples
Architects and engineers often use blueprints to communicate designs. Knowing how to convert measurements from a small-scale drawing to full-size reality is crucial for construction. For example, if an interior designer plans a floor layout, they can use scale drawings to calculate the exact amount of flooring or paint needed for a real room, ensuring all measurements are accurate and professional.