Given ABC -DBE, find EB ### Problem StatementGiven triangles $\triangle ABC \sim \triangle DBE$, find the length of segment $EB$.### Diagram DescriptionThe 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 $\triangle DBE$.### ExplanationTo 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 Solve1. Determine the ratios from the similar triangles: \[ \frac{AB}{DB} = \frac{BC}{BE} \]2. Substitute the known values into the ratio and solve for $EB$: \[ \frac{11.2 + 28}{28} = \frac{35}{EB} \]### CalculationFirst, 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.

Given that the triangles ABC and DBE are similar. We have to find the measure of BE.

Answered: Given ABC -DBE, find EB

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Given ABC -DBE, find EB

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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Question

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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.

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