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Solve for x. The triangles in each pair are similar. 20) ΔJKL ~ ΔΑΒC 56 J L 58° 3x - 12 K C B 3/58° A A) 12 C) 7 7 B) 11 D) 13

Solve for x. The triangles in each pair are similar. 20) ΔJKL ~ ΔΑΒC 56 J L 58° 3x - 12 K C B 3/58° A A) 12 C) 7 7 B) 11 D) 13

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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how would you do 20? would you use the law of cosines?
### Solving Similar Triangles **Problem Statement:** Solve for \( x \). The triangles in each pair are similar. #### Question 20: Given the similar triangles \( \triangle JKL \sim \triangle ABC \): **Triangle \( \triangle JKL \):** - Angle \( J \): 58° - \( \overline{LJ} \): 56 (Length of side between points L and J) - \( \overline{JK} \): \( 3x - 12 \) (Length of side between points J and K) **Triangle \( \triangle ABC \):** - Angle \( B \): 58° - \( \overline{AB} \): 3 (Length of side between points A and B) - \( \overline{BC} \): 7 (Length of side between points B and C) **Options:** - A) 12 - B) 11 - C) 7 - D) 13 **Diagram Explanation:** 1. The problem contains diagrams of two triangles, \( \triangle JKL \) and \( \triangle ABC \), which are stated to be similar. 2. For \( \triangle JKL \): - The side \( \overline{LJ} \) is labeled with a length of 56. - Angle \( J \) is given as 58°. - The side \( \overline{JK} \) is labeled with an expression \( 3x - 12 \). 3. For \( \triangle ABC \): - The side \( \overline{AB} \) is labeled with a length of 3. - Angle \( B \) is given as 58°. - The side \( \overline{BC} \) is labeled with a length of 7. Since the triangles are similar, the corresponding sides are proportional. This problem asks you to find the value of \( x \) using this property. **How to Solve:** 1. Set up the ratio of the corresponding sides since the triangles are similar: \[ \frac{\overline{LJ}}{\overline{AB}} = \frac{\overline{JK}}{\overline{BC}} \] 2. Substitute the known values into the proportion: \[ \frac{56}{3} = \frac{3
Transcribed Image Text:### Solving Similar Triangles **Problem Statement:** Solve for \( x \). The triangles in each pair are similar. #### Question 20: Given the similar triangles \( \triangle JKL \sim \triangle ABC \): **Triangle \( \triangle JKL \):** - Angle \( J \): 58° - \( \overline{LJ} \): 56 (Length of side between points L and J) - \( \overline{JK} \): \( 3x - 12 \) (Length of side between points J and K) **Triangle \( \triangle ABC \):** - Angle \( B \): 58° - \( \overline{AB} \): 3 (Length of side between points A and B) - \( \overline{BC} \): 7 (Length of side between points B and C) **Options:** - A) 12 - B) 11 - C) 7 - D) 13 **Diagram Explanation:** 1. The problem contains diagrams of two triangles, \( \triangle JKL \) and \( \triangle ABC \), which are stated to be similar. 2. For \( \triangle JKL \): - The side \( \overline{LJ} \) is labeled with a length of 56. - Angle \( J \) is given as 58°. - The side \( \overline{JK} \) is labeled with an expression \( 3x - 12 \). 3. For \( \triangle ABC \): - The side \( \overline{AB} \) is labeled with a length of 3. - Angle \( B \) is given as 58°. - The side \( \overline{BC} \) is labeled with a length of 7. Since the triangles are similar, the corresponding sides are proportional. This problem asks you to find the value of \( x \) using this property. **How to Solve:** 1. Set up the ratio of the corresponding sides since the triangles are similar: \[ \frac{\overline{LJ}}{\overline{AB}} = \frac{\overline{JK}}{\overline{BC}} \] 2. Substitute the known values into the proportion: \[ \frac{56}{3} = \frac{3
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