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d the area of AABC is 18, then what is the

d the area of AABC is 18, then what is the

Elementary Geometry For College Students, 7e
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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I need 7 to be chrcked if correct and help with 8
**Transcription for Educational Website** ### Problem 7 **Given:** \(\triangle ABC \sim \triangle DEF\) and the perimeter of \(\triangle DEF\) is 36. **Question:** What is the length of the longest side of \(\triangle DEF\)? **Solution:** - **Side Ratios and Lengths:** - Side \(A\): \(\frac{5}{x}\) - Side \(B\): \(\frac{27}{36}\) - Side \(C\): \(\frac{6}{x}\) - **Setup Equations:** - \(5 + 27 + 6 = 27 \rightarrow x = 12\) - Length of longest side is marked as 21. --- ### Problem 8 **Given:** \(\triangle ABC \sim \triangle XYZ\) and the area of \(\triangle ABC\) is 18. **Question:** What is the area of \(\triangle XYZ\)? **Solution:** - **Triangles Similarity:** - \(\triangle ABC\) with \(\triangle XYZ\) - Given \(\triangle ABC\) area = 18. - **Ratios and Calculations:** - Side \(A\): \(\frac{32}{18} = \frac{z}{x}\) - Area calculation shows answer marked as 32. --- ### Problem 9 **Accompanying Diagram Explanation:** The diagram shows a section of the city of Tacoma, with parallel streets labeled as High Road, State Street, and Main Street. - Ridge Road is perpendicular to these streets. - The distance between the intersections of Ridge Road and State Street is given as 5 miles. - **Question:** What is the distance between the intersection of Ridge Road and Main Street and the railroad tracks crossing Main Street? **Note:** Solution must show work for any calculations.
Transcribed Image Text:**Transcription for Educational Website** ### Problem 7 **Given:** \(\triangle ABC \sim \triangle DEF\) and the perimeter of \(\triangle DEF\) is 36. **Question:** What is the length of the longest side of \(\triangle DEF\)? **Solution:** - **Side Ratios and Lengths:** - Side \(A\): \(\frac{5}{x}\) - Side \(B\): \(\frac{27}{36}\) - Side \(C\): \(\frac{6}{x}\) - **Setup Equations:** - \(5 + 27 + 6 = 27 \rightarrow x = 12\) - Length of longest side is marked as 21. --- ### Problem 8 **Given:** \(\triangle ABC \sim \triangle XYZ\) and the area of \(\triangle ABC\) is 18. **Question:** What is the area of \(\triangle XYZ\)? **Solution:** - **Triangles Similarity:** - \(\triangle ABC\) with \(\triangle XYZ\) - Given \(\triangle ABC\) area = 18. - **Ratios and Calculations:** - Side \(A\): \(\frac{32}{18} = \frac{z}{x}\) - Area calculation shows answer marked as 32. --- ### Problem 9 **Accompanying Diagram Explanation:** The diagram shows a section of the city of Tacoma, with parallel streets labeled as High Road, State Street, and Main Street. - Ridge Road is perpendicular to these streets. - The distance between the intersections of Ridge Road and State Street is given as 5 miles. - **Question:** What is the distance between the intersection of Ridge Road and Main Street and the railroad tracks crossing Main Street? **Note:** Solution must show work for any calculations.
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