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The two triangles are similar. What is the value of x? Enter your answer in the box. X = R % T G 6 8 4 3 1 2 12 3 J K L 4 3x + 1 4x 6 7

The two triangles are similar. What is the value of x? Enter your answer in the box. X = R % T G 6 8 4 3 1 2 12 3 J K L 4 3x + 1 4x 6 7

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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**The two triangles are similar.** **What is the value of x?** **Enter your answer in the box.** \[ x = [ \_\_\_ ] \] --- **Figure Explanation:** The image displays two right-angled triangles that are similar to each other. The smaller triangle has one leg labeled as 3 units and the hypotenuse labeled as 12 units. The larger triangle has one leg labeled as \( 3x + 1 \) and the hypotenuse labeled as \( 4x \). --- **Concept:** To find the value of \( x \), we need to use the properties of similar triangles. In similar triangles, the ratios of the corresponding sides are equal. For two similar triangles: \[ \frac{\text{Side 1 of Triangle A}}{\text{Side 1 of Triangle B}} = \frac{\text{Side 2 of Triangle A}}{\text{Side 2 of Triangle B}} = \frac{\text{Side 3 of Triangle A}}{\text{Side 3 of Triangle B}} \] In this problem, we can equate the ratios of their corresponding sides to solve for \( x \).
Transcribed Image Text:**The two triangles are similar.** **What is the value of x?** **Enter your answer in the box.** \[ x = [ \_\_\_ ] \] --- **Figure Explanation:** The image displays two right-angled triangles that are similar to each other. The smaller triangle has one leg labeled as 3 units and the hypotenuse labeled as 12 units. The larger triangle has one leg labeled as \( 3x + 1 \) and the hypotenuse labeled as \( 4x \). --- **Concept:** To find the value of \( x \), we need to use the properties of similar triangles. In similar triangles, the ratios of the corresponding sides are equal. For two similar triangles: \[ \frac{\text{Side 1 of Triangle A}}{\text{Side 1 of Triangle B}} = \frac{\text{Side 2 of Triangle A}}{\text{Side 2 of Triangle B}} = \frac{\text{Side 3 of Triangle A}}{\text{Side 3 of Triangle B}} \] In this problem, we can equate the ratios of their corresponding sides to solve for \( x \).
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