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12. If ATSR ATFE, find the perimeter of ATFE. F E R 40 54 T 25 22 S

12. If ATSR ATFE, find the perimeter of ATFE. F E R 40 54 T 25 22 S

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 10E
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### Problem 12: Similar Triangles **Given:** Triangles \( \triangle TSR \sim \triangle TFE \). **Task:** Find the perimeter of \( \triangle TFE \). **Diagram Explanation:** - The diagram shows two triangles \( \triangle TSR \) and \( \triangle TFE \) which are similar. - The sides of \( \triangle TSR \) are labeled as \( TR = 40 \), \( RS = 54 \), and \( TS = 22 \). - The side \( FE \) in \( \triangle TFE \) is labeled as 25. **Solution Approach:** 1. **Understand Similarity:** - Since the triangles are similar, corresponding sides are proportional. - Use the proportionality to find unknown lengths of \( \triangle TFE \). 2. **Set Up Proportions:** - \( \frac{TS}{TF} = \frac{TR}{TE} = \frac{RS}{FE} \). 3. **Find Unknown Lengths:** - Given \( TE = 25 \) and \( TS = 22 \), use the similarity ratio to calculate \( TF \) and \( FE \). 4. **Calculate the Perimeter of \( \triangle TFE \):** - Add the lengths of \( TF \), \( TE \), and \( FE \) to get the perimeter. **Note:** Ensure to follow the correct algebraic steps considering the proportional relationships and calculations to determine the perimeter accurately.
Transcribed Image Text:### Problem 12: Similar Triangles **Given:** Triangles \( \triangle TSR \sim \triangle TFE \). **Task:** Find the perimeter of \( \triangle TFE \). **Diagram Explanation:** - The diagram shows two triangles \( \triangle TSR \) and \( \triangle TFE \) which are similar. - The sides of \( \triangle TSR \) are labeled as \( TR = 40 \), \( RS = 54 \), and \( TS = 22 \). - The side \( FE \) in \( \triangle TFE \) is labeled as 25. **Solution Approach:** 1. **Understand Similarity:** - Since the triangles are similar, corresponding sides are proportional. - Use the proportionality to find unknown lengths of \( \triangle TFE \). 2. **Set Up Proportions:** - \( \frac{TS}{TF} = \frac{TR}{TE} = \frac{RS}{FE} \). 3. **Find Unknown Lengths:** - Given \( TE = 25 \) and \( TS = 22 \), use the similarity ratio to calculate \( TF \) and \( FE \). 4. **Calculate the Perimeter of \( \triangle TFE \):** - Add the lengths of \( TF \), \( TE \), and \( FE \) to get the perimeter. **Note:** Ensure to follow the correct algebraic steps considering the proportional relationships and calculations to determine the perimeter accurately.
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