Question
2. A fish in an aquarium is 4 feet long. A scale model of the fish is 2 inches long. What is the scale factor? HINT: Determine how many inches are in 4 feet. Then use that new amount to calculate the scale factor. (Use your notes as a guide!)
Ask by Dunn Munoz. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The scale factor is 1:24.
Solution
1. Convert the actual fish length from feet to inches:
\[
4 \text{ ft} \times 12 \frac{\text{in}}{\text{ft}} = 48 \text{ in}
\]
2. The scale model fish length is \(2\) inches.
3. Set up the scale factor as the ratio of the model length to the actual fish length:
\[
\text{Scale Factor} = \frac{2 \text{ in}}{48 \text{ in}} = \frac{1}{24}
\]
Thus, the scale factor is \(\frac{1}{24}\).
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Simplify this solution Beyond the Answer
To find the scale factor, first convert the 4 feet into inches. Since there are 12 inches in a foot, you multiply 4 by 12, yielding 48 inches. Now, to find the scale factor, divide the model's length (2 inches) by the original length in inches (48 inches): 2 ÷ 48 = 1/24. This means the scale model is 1/24th the size of the actual fish! Understanding scale factors is crucial in fields like architecture and design. When creating blueprints, designers use scale models to represent larger structures while maintaining proportionality. This helps visualize projects from a practical standpoint, offering insights into dimensions and aesthetics before the construction begins!
