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The triangle below is equilateral. Find the length of side x in simplest radical form with a rational denominator. X 5√3 3 5√2 5√2 2 ○ 2.5 5

The triangle below is equilateral. Find the length of side x in simplest radical form with a rational denominator. X 5√3 3 5√2 5√2 2 ○ 2.5 5

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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**Problem Statement:** The triangle below is equilateral. Find the length of side \( x \) in simplest radical form with a rational denominator. **Diagram Explanation:** - The diagram shows an equilateral triangle with a side length divided by an altitude. - The altitude forms two 30-60-90 right triangles within the equilateral triangle. - The length given along the altitude is 5. - The segment of the side length opposite the 30-degree angle (half of one side of the equilateral triangle) is denoted as \( x \). - The right angle is marked near the vertex connecting the altitude and the base. **Answer Choices:** Below the diagram are multiple-choice answers to the problem statement: - \( \frac{5\sqrt{3}}{3} \) (selected answer) - \( 5\sqrt{2} \) - \( \frac{5\sqrt{2}}{2} \) - 2.5
Transcribed Image Text:**Problem Statement:** The triangle below is equilateral. Find the length of side \( x \) in simplest radical form with a rational denominator. **Diagram Explanation:** - The diagram shows an equilateral triangle with a side length divided by an altitude. - The altitude forms two 30-60-90 right triangles within the equilateral triangle. - The length given along the altitude is 5. - The segment of the side length opposite the 30-degree angle (half of one side of the equilateral triangle) is denoted as \( x \). - The right angle is marked near the vertex connecting the altitude and the base. **Answer Choices:** Below the diagram are multiple-choice answers to the problem statement: - \( \frac{5\sqrt{3}}{3} \) (selected answer) - \( 5\sqrt{2} \) - \( \frac{5\sqrt{2}}{2} \) - 2.5
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