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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Question
![### Problem Statement:
Given two similar triangles, ∆ACB and ∆FED, find the value of \( x \).
### Diagram:
The problem provides two triangles labeled ∆ACB and ∆FED.
**Triangle ACB:**
- Side AB = \( x + 4.4 \)
- Side BC = 9
- Side AC = 23.5
**Triangle FED:**
- Side ED = 22.5
- The remaining side lengths and angle measurements are not provided.
### Relationship:
∆ACB ~ ∆FED (indicating that the triangles ACB and FED are similar).
### Instructions:
- Identify the proportion between the corresponding sides of the similar triangles.
- Use this proportion to find the unknown value \( x \).
### Form:
There is an input box labeled "Type a number..." where you are expected to enter the value of \( x \).
### Actions:
- Once you have calculated the value of \( x \), enter it in the provided input field.
- Click on the "SUBMIT" button to submit your answer.
### Calculation:
Since the triangles are similar, the ratio of corresponding sides are equal. Set up a proportion to solve for \( x \).
For example,
\[
\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}
\]
Use this relationship to find \( x \).
### Submission:
Ensure your answer is a numerical value before submitting.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa53c426-a760-4829-b362-653d3877b060%2F38da3629-dafb-4031-9974-a9b9c2f10b28%2F1t2c466_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
Given two similar triangles, ∆ACB and ∆FED, find the value of \( x \).
### Diagram:
The problem provides two triangles labeled ∆ACB and ∆FED.
**Triangle ACB:**
- Side AB = \( x + 4.4 \)
- Side BC = 9
- Side AC = 23.5
**Triangle FED:**
- Side ED = 22.5
- The remaining side lengths and angle measurements are not provided.
### Relationship:
∆ACB ~ ∆FED (indicating that the triangles ACB and FED are similar).
### Instructions:
- Identify the proportion between the corresponding sides of the similar triangles.
- Use this proportion to find the unknown value \( x \).
### Form:
There is an input box labeled "Type a number..." where you are expected to enter the value of \( x \).
### Actions:
- Once you have calculated the value of \( x \), enter it in the provided input field.
- Click on the "SUBMIT" button to submit your answer.
### Calculation:
Since the triangles are similar, the ratio of corresponding sides are equal. Set up a proportion to solve for \( x \).
For example,
\[
\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}
\]
Use this relationship to find \( x \).
### Submission:
Ensure your answer is a numerical value before submitting.
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