Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28bd164b-15c0-4281-9396-dc8e872bf440%2F94adf59c-7728-4b0a-932b-96271562db5f%2Fyfn9tvm_processed.jpeg&w=3840&q=75)
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.
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