
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
thumb_up100%
Given ABC -DBE, find EB
![### Problem Statement
Given triangles \(\triangle ABC \sim \triangle DBE\), find the length of segment \(EB\).
### Diagram Description
The diagram depicts two similar triangles: \(\triangle ABC\) and \(\triangle DBE\). Here are the details:
- \(\triangle ABC\) is a larger triangle with \(AD\) as part of one side, \(6\).
- \(\triangle DBE\) is a smaller, nested triangle within \(\triangle ABC\), sharing the angle at vertex \(B\).
- The length \(AD\) is labeled as 11.2 units.
- The length \(DB\) is labeled as 28 units.
- The length \(BC\) is labeled as 35 units.
- The line segment \(AE\) within \(\triangle ABC\) meets line segment \(DE\) from within \(\triangle DBE\).
### Explanation
To find \(EB\), you would use the properties of similar triangles. When two triangles are similar, the ratios of corresponding sides are equal.
1. First, identify the corresponding sides between \(\triangle ABC\) and \(\triangle DBE\).
2. Use the proportionality of the sides to set up equations where segments of interest appear.
3. Solve for the unknown length (in this case, \(EB\)) using the known lengths.
Given:
- \(AD = 11.2\)
- \(DB = 28\)
- \(BC = 35\)
### Steps to Solve
1. Determine the ratios from the similar triangles:
\[
\frac{AB}{DB} = \frac{BC}{BE}
\]
2. Substitute the known values into the ratio and solve for \(EB\):
\[
\frac{11.2 + 28}{28} = \frac{35}{EB}
\]
### Calculation
First, we calculate \(AB\):
\[
AB = AD + DB = 11.2 + 28 = 39.2
\]
Now we set up the proportion:
\[
\frac{39.2}{28} = \frac{35}{EB}
\]
Cross-multiplying to solve for \(EB\):
\[
39.2 \times EB = 28 \times 35
\]
\[
39.](https://content.bartleby.com/qna-images/question/28bd164b-15c0-4281-9396-dc8e872bf440/94adf59c-7728-4b0a-932b-96271562db5f/yfn9tvm_thumbnail.jpeg)
Transcribed Image Text:### Problem Statement
Given triangles \(\triangle ABC \sim \triangle DBE\), find the length of segment \(EB\).
### Diagram Description
The diagram depicts two similar triangles: \(\triangle ABC\) and \(\triangle DBE\). Here are the details:
- \(\triangle ABC\) is a larger triangle with \(AD\) as part of one side, \(6\).
- \(\triangle DBE\) is a smaller, nested triangle within \(\triangle ABC\), sharing the angle at vertex \(B\).
- The length \(AD\) is labeled as 11.2 units.
- The length \(DB\) is labeled as 28 units.
- The length \(BC\) is labeled as 35 units.
- The line segment \(AE\) within \(\triangle ABC\) meets line segment \(DE\) from within \(\triangle DBE\).
### Explanation
To find \(EB\), you would use the properties of similar triangles. When two triangles are similar, the ratios of corresponding sides are equal.
1. First, identify the corresponding sides between \(\triangle ABC\) and \(\triangle DBE\).
2. Use the proportionality of the sides to set up equations where segments of interest appear.
3. Solve for the unknown length (in this case, \(EB\)) using the known lengths.
Given:
- \(AD = 11.2\)
- \(DB = 28\)
- \(BC = 35\)
### Steps to Solve
1. Determine the ratios from the similar triangles:
\[
\frac{AB}{DB} = \frac{BC}{BE}
\]
2. Substitute the known values into the ratio and solve for \(EB\):
\[
\frac{11.2 + 28}{28} = \frac{35}{EB}
\]
### Calculation
First, we calculate \(AB\):
\[
AB = AD + DB = 11.2 + 28 = 39.2
\]
Now we set up the proportion:
\[
\frac{39.2}{28} = \frac{35}{EB}
\]
Cross-multiplying to solve for \(EB\):
\[
39.2 \times EB = 28 \times 35
\]
\[
39.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 2 steps

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education

Algebra and Trigonometry (6th Edition)
Algebra
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:PEARSON

Contemporary Abstract Algebra
Algebra
ISBN:9781305657960
Author:Joseph Gallian
Publisher:Cengage Learning

Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning

Algebra And Trigonometry (11th Edition)
Algebra
ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON

Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press

College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education