24 The triangles are similar. Solve for x. 6. 8.

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
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### Similar Triangles Problem

**Problem Statement:**

24. The triangles are similar. Solve for \( x \).

**Diagrams:**

There are two triangles shown. The smaller, left triangle has side lengths labeled 6, 8, and 4. The larger, right triangle has side lengths labeled \( x \), \( y \), and 6.

**Answer Choices:**

- A: 12
- B: 4.5
- C: 9
- D: 8

**Explanation:**

Since the triangles are similar, their corresponding sides are proportional. Therefore, we can set up a proportion using the corresponding sides of the triangles. 

We compare the side of length 6 in the smaller triangle to the side of length \( x \) in the larger triangle, and the side of length 8 in the smaller triangle to the side of length \( y \) in the larger triangle.

Given the side lengths 6 (of the smaller triangle) and x (of the larger triangle) are corresponding sides, and the sides of length 8 (of the smaller triangle) and y (of the larger triangle) are corresponding sides, we use the ratio:
\[
\frac{6}{x} = \frac{8}{y}
\]
We can solve this to isolate \( x \). 

Note: You would typically find the full solution by also using the third side pair (4 and 6) if y were needed, but in this problem, we only need to find \( x \) directly using the given options and the proportion mentioned for similar triangles.
Transcribed Image Text:### Similar Triangles Problem **Problem Statement:** 24. The triangles are similar. Solve for \( x \). **Diagrams:** There are two triangles shown. The smaller, left triangle has side lengths labeled 6, 8, and 4. The larger, right triangle has side lengths labeled \( x \), \( y \), and 6. **Answer Choices:** - A: 12 - B: 4.5 - C: 9 - D: 8 **Explanation:** Since the triangles are similar, their corresponding sides are proportional. Therefore, we can set up a proportion using the corresponding sides of the triangles. We compare the side of length 6 in the smaller triangle to the side of length \( x \) in the larger triangle, and the side of length 8 in the smaller triangle to the side of length \( y \) in the larger triangle. Given the side lengths 6 (of the smaller triangle) and x (of the larger triangle) are corresponding sides, and the sides of length 8 (of the smaller triangle) and y (of the larger triangle) are corresponding sides, we use the ratio: \[ \frac{6}{x} = \frac{8}{y} \] We can solve this to isolate \( x \). Note: You would typically find the full solution by also using the third side pair (4 and 6) if y were needed, but in this problem, we only need to find \( x \) directly using the given options and the proportion mentioned for similar triangles.
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