Math Problem Statement

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

Solution

The problem asks to find the length of segment LMLM given the total length KM=22KM = 22, where KL=xKL = x and LM=3xLM = 3x.

Step-by-step Solution:

  1. The total length KMKM is given as: KL+LM=22KL + LM = 22 From the diagram, KL=xKL = x and LM=3xLM = 3x, so: x+3x=22x + 3x = 22

  2. Simplifying the equation: 4x=224x = 22

  3. Solving for xx: x=224=5.5x = \frac{22}{4} = 5.5

  4. Now, LM=3xLM = 3x, so: LM=3(5.5)=16.5LM = 3(5.5) = 16.5

Final Answer:

The length of segment LMLM 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 KLKL?
  2. What if the total length of KMKM was different, say 30 units?
  3. Can you write a general formula to find LMLM if the ratio between KLKL and LMLM changes?
  4. How would this problem change if LM=2xLM = 2x instead of 3x3x?
  5. What if both KLKL and LMLM were expressed as different algebraic terms?

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

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

KL + LM = KM
x + 3x = 22

Theorems

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Suitable Grade Level

Grades 6-8