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
Related questions
Question
![### Problem 25:
**Question:**
If triangles \( \triangle BCA \) and \( \triangle DEA \) are similar, what is the value of \( x \)?
**Diagram Description:**
- Two right triangles, \( \triangle BCA \) and \( \triangle DEA \), are shown in the diagram.
- Triangle \( \triangle BCA \) has:
- Base \( CA = 25 \) ft.
- Height \( BC = x \).
- A right angle at \( C \).
- Triangle \( \triangle DEA \) has:
- Base \( EA = 5 \) ft.
- Height \( DE = 6 \) ft.
- A right angle at \( A \).
**Answer Options:**
- \( \text{A. } 19 \text{ ft.} \)
- \( \text{B. } 5 \text{ ft.} \)
- \( \text{C. } 25 \text{ ft.} \)
- \( \text{D. } 30 \text{ ft.} \)
**Explanation:**
Since the triangles \( \triangle BCA \) and \( \triangle DEA \) are similar, their corresponding sides are proportional.
\[
\frac{BC}{DE} = \frac{CA}{EA}
\]
Substitute the known values:
\[
\frac{x}{6} = \frac{25}{5}
\]
Simplify \( \frac{25}{5} \) to get 5:
\[
\frac{x}{6} = 5
\]
Solve for \( x \):
\[
x = 6 \times 5 = 30 \text{ ft.}
\]
**Correct Answer:**
- \( \text{D. } 30 \text{ ft.} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09a470f7-0e80-48df-a8b7-f2bdb6e02707%2F23df0e2d-d654-4bf3-b297-e96d73ec8df4%2Fcackyos_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 25:
**Question:**
If triangles \( \triangle BCA \) and \( \triangle DEA \) are similar, what is the value of \( x \)?
**Diagram Description:**
- Two right triangles, \( \triangle BCA \) and \( \triangle DEA \), are shown in the diagram.
- Triangle \( \triangle BCA \) has:
- Base \( CA = 25 \) ft.
- Height \( BC = x \).
- A right angle at \( C \).
- Triangle \( \triangle DEA \) has:
- Base \( EA = 5 \) ft.
- Height \( DE = 6 \) ft.
- A right angle at \( A \).
**Answer Options:**
- \( \text{A. } 19 \text{ ft.} \)
- \( \text{B. } 5 \text{ ft.} \)
- \( \text{C. } 25 \text{ ft.} \)
- \( \text{D. } 30 \text{ ft.} \)
**Explanation:**
Since the triangles \( \triangle BCA \) and \( \triangle DEA \) are similar, their corresponding sides are proportional.
\[
\frac{BC}{DE} = \frac{CA}{EA}
\]
Substitute the known values:
\[
\frac{x}{6} = \frac{25}{5}
\]
Simplify \( \frac{25}{5} \) to get 5:
\[
\frac{x}{6} = 5
\]
Solve for \( x \):
\[
x = 6 \times 5 = 30 \text{ ft.}
\]
**Correct Answer:**
- \( \text{D. } 30 \text{ ft.} \)
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