Figure JKLMN and figure PQRST, shown below, are similar figures. K L M P R N The scale factor of figure JKLMN to figure PQRST is 3:2. If KL = 18 cm and MN = 30 cm, what is the length of side ST? OA. 45 cm В. 20 cm Oc. 27 cm D. 12 cm
Figure JKLMN and figure PQRST, shown below, are similar figures. K L M P R N The scale factor of figure JKLMN to figure PQRST is 3:2. If KL = 18 cm and MN = 30 cm, what is the length of side ST? OA. 45 cm В. 20 cm Oc. 27 cm D. 12 cm
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter12: Angle Relationships And Transformations
Section12.5: Reflections And Symmetry
Problem 20E
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![### Similar Figures: A Scale Factor Question
#### Problem Statement
Figures JKLMN and PQRST, shown below, are similar figures:
![Image of Two Similar Figures: JKLMN and PQRST.
Figure JKLMN is a larger quadrilateral with vertices labeled K, L, M, N, and J.
Figure PQRST is a smaller quadrilateral with vertices labeled P, Q, R, S, and T.
The smaller figure is highlighted with a red color.]
**The scale factor of figure JKLMN to figure PQRST is 3:2. If \( KL = 18 \) cm and \( MN = 30 \) cm, what is the length of side \( ST \)?**
#### Answer Choices:
- **A.** 45 cm
- **B.** 20 cm
- **C.** 27 cm
- **D.** 12 cm
#### Solution Process:
1. **Understanding the Scale Factor**:
The scale factor between the two figures is given as \( 3:2 \). This means every dimension in figure JKLMN is \( \frac{3}{2} \) times the corresponding dimension in figure PQRST.
2. **Identifying the Corresponding Sides**:
- \( KL \) and \( ST \) are corresponding sides in the two figures.
- The length of \( KL \) is 18 cm.
3. **Relationship Using Scale Factor**:
Since \( JKLMN \) is larger and the scale factor is from JKLMN to PQRST, we'll use the scale factor to find the length of \( ST \):
\[
\frac{JKLMN}{PQRST} = \frac{KL}{ST} = \frac{3}{2}
\]
Therefore,
\[
ST = \frac{2}{3} \times KL
\]
4. **Calculate \( ST \)**
Using the given \( KL = 18 \) cm:
\[
ST = \frac{2}{3} \times 18 = 12 \text{ cm}
\]
Hence, the length of side \( ST \) is \( 12 \) cm.
#### Correct Answer:
- **D. 12 cm**
This solution illustrates the method of using scale factors to determine the corresponding dimensions in similar geometric figures.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b4ac02d-8fa9-4cd1-ad8a-49ffeef4197d%2F29d98191-1d07-4e6a-8435-8c2e9baab11f%2F6ig2o37_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Similar Figures: A Scale Factor Question
#### Problem Statement
Figures JKLMN and PQRST, shown below, are similar figures:
![Image of Two Similar Figures: JKLMN and PQRST.
Figure JKLMN is a larger quadrilateral with vertices labeled K, L, M, N, and J.
Figure PQRST is a smaller quadrilateral with vertices labeled P, Q, R, S, and T.
The smaller figure is highlighted with a red color.]
**The scale factor of figure JKLMN to figure PQRST is 3:2. If \( KL = 18 \) cm and \( MN = 30 \) cm, what is the length of side \( ST \)?**
#### Answer Choices:
- **A.** 45 cm
- **B.** 20 cm
- **C.** 27 cm
- **D.** 12 cm
#### Solution Process:
1. **Understanding the Scale Factor**:
The scale factor between the two figures is given as \( 3:2 \). This means every dimension in figure JKLMN is \( \frac{3}{2} \) times the corresponding dimension in figure PQRST.
2. **Identifying the Corresponding Sides**:
- \( KL \) and \( ST \) are corresponding sides in the two figures.
- The length of \( KL \) is 18 cm.
3. **Relationship Using Scale Factor**:
Since \( JKLMN \) is larger and the scale factor is from JKLMN to PQRST, we'll use the scale factor to find the length of \( ST \):
\[
\frac{JKLMN}{PQRST} = \frac{KL}{ST} = \frac{3}{2}
\]
Therefore,
\[
ST = \frac{2}{3} \times KL
\]
4. **Calculate \( ST \)**
Using the given \( KL = 18 \) cm:
\[
ST = \frac{2}{3} \times 18 = 12 \text{ cm}
\]
Hence, the length of side \( ST \) is \( 12 \) cm.
#### Correct Answer:
- **D. 12 cm**
This solution illustrates the method of using scale factors to determine the corresponding dimensions in similar geometric figures.
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