Question
Find the scale factor of each problem below. \( \begin{array}{lll}\text { 12. } 9 \text { inches: } 72 \text { inches } & \text { 13. } 5 \mathrm{~cm} \text { to } 145 \mathrm{~cm} & 14.2 \mathrm{ft:} 27 \mathrm{ft}\end{array} \)
Ask by Cox Fernandez. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
- **Problem 12:** 8
- **Problem 13:** 29
- **Problem 14:** 13.5
Solution
To find the **scale factor** for each pair of measurements, you divide the larger measurement by the smaller one. The scale factor indicates how much larger (or smaller) one measurement is compared to the other.
### Problem 12
**Given:** 9 inches : 72 inches
**Scale Factor Calculation:**
\[
\text{Scale Factor} = \frac{72}{9} = 8
\]
**Scale Factor:** **8**
---
### Problem 13
**Given:** 5 cm : 145 cm
**Scale Factor Calculation:**
\[
\text{Scale Factor} = \frac{145}{5} = 29
\]
**Scale Factor:** **29**
---
### Problem 14
**Given:** 2 ft : 27 ft
**Scale Factor Calculation:**
\[
\text{Scale Factor} = \frac{27}{2} = 13.5
\]
**Scale Factor:** **13.5**
---
**Summary of Scale Factors:**
- **Problem 12:** 8
- **Problem 13:** 29
- **Problem 14:** 13.5
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Mind Expander
To find the scale factor, you need to divide the second measurement by the first. For the first problem, \( \frac{72 \text{ inches}}{9 \text{ inches}} = 8 \). So, the scale factor is 8. For the second problem, \( \frac{145 \text{ cm}}{5 \text{ cm}} = 29 \). Thus, the scale factor is 29. For the third problem, \( \frac{27 \text{ ft}}{14.2 \text{ ft}} \approx 1.9028 \). Therefore, the scale factor is approximately 1.90.