Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![**Triangle Similarity Problem**
**Problem:**
∆XYZ has side lengths in the ratio 3:4:5. Which group of three lengths represents a triangle similar to ∆XYZ?
- ⭘ 4, 6, 7
- ⭘ 6, 8, 12
- ⭘ 18, 24, 45
- ⭘ 36, 48, 60
**Solution Explanation:**
To determine which group of three lengths represents a triangle similar to ∆XYZ, we need to find sets of lengths that maintain the ratio 3:4:5.
1. **Check the first set: 4, 6, 7**
\[
\frac{4}{3} \neq \frac{6}{4} \neq \frac{7}{5}
\]
This set does not maintain the ratio 3:4:5.
2. **Check the second set: 6, 8, 12**
\[
\frac{6}{3} = 2, \quad \frac{8}{4} = 2, \quad \frac{12}{5} = 2.4
\]
This set does not maintain the ratio 3:4:5.
3. **Check the third set: 18, 24, 45**
\[
\frac{18}{3} = 6, \quad \frac{24}{4} = 6, \quad \frac{45}{5} = 9
\]
This set does not maintain the ratio 3:4:5.
4. **Check the fourth set: 36, 48, 60**
\[
\frac{36}{3} = 12, \quad \frac{48}{4} = 12, \quad \frac{60}{5} = 12
\]
This set maintains the ratio 3:4:5.
Therefore, the group of lengths 36, 48, 60 represents a triangle similar to ∆XYZ.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F72102c8b-d9ea-44e0-a86b-3888accb1152%2Faead25f8-12be-44ee-a858-75121edd0844%2F76ivude_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Triangle Similarity Problem**
**Problem:**
∆XYZ has side lengths in the ratio 3:4:5. Which group of three lengths represents a triangle similar to ∆XYZ?
- ⭘ 4, 6, 7
- ⭘ 6, 8, 12
- ⭘ 18, 24, 45
- ⭘ 36, 48, 60
**Solution Explanation:**
To determine which group of three lengths represents a triangle similar to ∆XYZ, we need to find sets of lengths that maintain the ratio 3:4:5.
1. **Check the first set: 4, 6, 7**
\[
\frac{4}{3} \neq \frac{6}{4} \neq \frac{7}{5}
\]
This set does not maintain the ratio 3:4:5.
2. **Check the second set: 6, 8, 12**
\[
\frac{6}{3} = 2, \quad \frac{8}{4} = 2, \quad \frac{12}{5} = 2.4
\]
This set does not maintain the ratio 3:4:5.
3. **Check the third set: 18, 24, 45**
\[
\frac{18}{3} = 6, \quad \frac{24}{4} = 6, \quad \frac{45}{5} = 9
\]
This set does not maintain the ratio 3:4:5.
4. **Check the fourth set: 36, 48, 60**
\[
\frac{36}{3} = 12, \quad \frac{48}{4} = 12, \quad \frac{60}{5} = 12
\]
This set maintains the ratio 3:4:5.
Therefore, the group of lengths 36, 48, 60 represents a triangle similar to ∆XYZ.
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