In the diagram below of triangle LMN,O is the midpoint of LN and P is the midpoint of MN .IFOP= –4+ 9x, and LM = 3+ 7x, what is the measure of LM? N P L M
In the diagram below of triangle LMN,O is the midpoint of LN and P is the midpoint of MN .IFOP= –4+ 9x, and LM = 3+ 7x, what is the measure of LM? N P L M
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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![**Geometry Problem: Calculating the Measure of LM in a Triangle**
**Problem Description:**
In the diagram below of triangle \( \triangle LMN \), \( O \) is the midpoint of \( \overline{LN} \) and \( P \) is the midpoint of \( \overline{MN} \). If \( OP = -4 + 9x \) and \( LM = 3 + 7x \), what is the measure of \( \overline{LM} \)?
**Diagram Explanation:**
The diagram shows triangle \( \triangle LMN \) with midpoints marked as follows:
- Point \( O \) is the midpoint of side \( \overline{LN} \).
- Point \( P \) is the midpoint of side \( \overline{MN} \).
**Equation and Calculation:**
1. Given:
\[ \overline{OP} = -4 + 9x \]
\[ \overline{LM} = 3 + 7x \]
2. The midsegment \( \overline{OP} \) of the triangle \( \triangle LMN \) is parallel to the third side \( \overline{LM} \) and half its length:
\[ \overline{OP} = \frac{1}{2} \overline{LM} = \frac{1}{2}(3 + 7x) \]
3. Set up the equation:
\[ -4 + 9x = \frac{1}{2}(3 + 7x) \]
**Answer Calculation Box:**
\[
\text{Answer: } \quad \overline{LM} = \quad \text{[Input Box to enter the calculated value]}
\]
[Submit Answer Button]
**Attempts:**
- Attempt 1 out of 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe58ad5a5-171d-4e22-97ee-d07765bc692c%2F687e3016-790f-45c2-9f45-8d29f5c8d1b4%2Fwddcber_processed.png&w=3840&q=75)
Transcribed Image Text:**Geometry Problem: Calculating the Measure of LM in a Triangle**
**Problem Description:**
In the diagram below of triangle \( \triangle LMN \), \( O \) is the midpoint of \( \overline{LN} \) and \( P \) is the midpoint of \( \overline{MN} \). If \( OP = -4 + 9x \) and \( LM = 3 + 7x \), what is the measure of \( \overline{LM} \)?
**Diagram Explanation:**
The diagram shows triangle \( \triangle LMN \) with midpoints marked as follows:
- Point \( O \) is the midpoint of side \( \overline{LN} \).
- Point \( P \) is the midpoint of side \( \overline{MN} \).
**Equation and Calculation:**
1. Given:
\[ \overline{OP} = -4 + 9x \]
\[ \overline{LM} = 3 + 7x \]
2. The midsegment \( \overline{OP} \) of the triangle \( \triangle LMN \) is parallel to the third side \( \overline{LM} \) and half its length:
\[ \overline{OP} = \frac{1}{2} \overline{LM} = \frac{1}{2}(3 + 7x) \]
3. Set up the equation:
\[ -4 + 9x = \frac{1}{2}(3 + 7x) \]
**Answer Calculation Box:**
\[
\text{Answer: } \quad \overline{LM} = \quad \text{[Input Box to enter the calculated value]}
\]
[Submit Answer Button]
**Attempts:**
- Attempt 1 out of 2.
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