https://file.aiquickdraw.com/mathbot/file/1726597812178bqfrscxb.jpg

The problem asks to find the length of segment \( LM \) given the total length \( KM = 22 \), where \( KL = x \) and \( LM = 3x \).

### Step-by-step Solution:

1. The total length \( KM \) is given as:
   \[
   KL + LM = 22
   \]
   From the diagram, \( KL = x \) and \( LM = 3x \), so:
   \[
   x + 3x = 22
   \]
   
2. Simplifying the equation:
   \[
   4x = 22
   \]
   
3. Solving for \( x \):
   \[
   x = \frac{22}{4} = 5.5
   \]

4. Now, \( LM = 3x \), so:
   \[
   LM = 3(5.5) = 16.5
   \]

### Final Answer:
The length of segment \( LM \) is **16.5 units**.

---

Would you like further details or have any questions? Here are five related questions to think about:

1. How would you find the length of segment \( KL \)?
2. What if the total length of \( KM \) was different, say 30 units?
3. Can you write a general formula to find \( LM \) if the ratio between \( KL \) and \( LM \) changes?
4. How would this problem change if \( LM = 2x \) instead of \( 3x \)?
5. What if both \( KL \) and \( LM \) were expressed as different algebraic terms?

**Tip:** Always double-check if the given equation can be simplified further before solving for variables.

Find the length of segment LM, given KM = 22, KL = x, and LM = 3x.

Learn how to find the length of segment LM in a linear equation problem where KM = 22, KL = x, and LM = 3x. This algebra problem is suitable for students in Grades 6-8 and covers key concepts such as forming and solving linear equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation