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LO bisects NLM, LM = 26, NO = 8, and LN = 18. What is the value of x? L N X M

LO bisects NLM, LM = 26, NO = 8, and LN = 18. What is the value of x? L N X M

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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LO bisects NLM, LM = 26, NO = 8, and LN = 18. What is the value of x?

A. x=84.5

B. x=58.5

C. x=11.6

D. x=5.5

## Problem Description: Given a diagram of triangle \( \triangle NLM \), where the ray \( \overrightarrow{LO} \) bisects \( \angle NLM \), the values of the triangle sides are as follows: - \( \overline{LM} = 26 \) - \( \overline{NO} = 8 \) - \( \overline{LN} = 18 \) The problem is to find the value of \( x \). ## Diagram Explanation: The diagram depicts a triangle \( \triangle NLM \) with the following points and sides: - \( L \) is one vertex at the base. - \( M \) is the other vertex at the base, forming side \( \overline{LM} \) with \( L \). - \( N \) is the top vertex connected to both \( L \) and \( M \). - A point \( O \) lies on side \( \overline{NM} \). - The ray \( \overrightarrow{LO} \) bisects the angle \( \angle NLM \). - \( x \) represents the segment \( \overline{OM} \). ## Solution: Given the angle bisector property, \[ \frac{\overline{LN}}{\overline{NM}} = \frac{\overline{LO}}{\overline{OM}} \] Since we know: - \( \overline{LN} = 18 \) - \( \overline{LM} = 26 \) - \( \overline{NO} = 8 \) - Let \( \overline{OM} = x \). The segment \( \overline{NM} \) can be partitioned as: \[ \overline{NM} = \overline{NO} + \overline{OM} \] \[ \overline{NM} = 8 + x \] Using the angle bisector theorem: \[ \frac{\overline{LN}}{\overline{NM}} = \frac{18}{8 + x} \] According to the theorem: \[ \frac{\overline{LN}}{\overline{NM}} = \frac{\overline{LM}}{\overline{OM}} \] So, \[ \frac{18}{8 + x} = \frac{26}{x} \] Cross-multiplying to solve for \( x \): \[
Transcribed Image Text:## Problem Description: Given a diagram of triangle \( \triangle NLM \), where the ray \( \overrightarrow{LO} \) bisects \( \angle NLM \), the values of the triangle sides are as follows: - \( \overline{LM} = 26 \) - \( \overline{NO} = 8 \) - \( \overline{LN} = 18 \) The problem is to find the value of \( x \). ## Diagram Explanation: The diagram depicts a triangle \( \triangle NLM \) with the following points and sides: - \( L \) is one vertex at the base. - \( M \) is the other vertex at the base, forming side \( \overline{LM} \) with \( L \). - \( N \) is the top vertex connected to both \( L \) and \( M \). - A point \( O \) lies on side \( \overline{NM} \). - The ray \( \overrightarrow{LO} \) bisects the angle \( \angle NLM \). - \( x \) represents the segment \( \overline{OM} \). ## Solution: Given the angle bisector property, \[ \frac{\overline{LN}}{\overline{NM}} = \frac{\overline{LO}}{\overline{OM}} \] Since we know: - \( \overline{LN} = 18 \) - \( \overline{LM} = 26 \) - \( \overline{NO} = 8 \) - Let \( \overline{OM} = x \). The segment \( \overline{NM} \) can be partitioned as: \[ \overline{NM} = \overline{NO} + \overline{OM} \] \[ \overline{NM} = 8 + x \] Using the angle bisector theorem: \[ \frac{\overline{LN}}{\overline{NM}} = \frac{18}{8 + x} \] According to the theorem: \[ \frac{\overline{LN}}{\overline{NM}} = \frac{\overline{LM}}{\overline{OM}} \] So, \[ \frac{18}{8 + x} = \frac{26}{x} \] Cross-multiplying to solve for \( x \): \[
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