Math Problem Statement

Find the value of x and the length of KM in the given line segment with KL = 12, LM = x - 5, and KM = 2x - 5.

Solution

We are asked to find the value of xx and the length of KM\overline{KM} in the given diagram. The line segment is divided into two parts:

  • KL=12KL = 12
  • LM=x5LM = x - 5
  • The total length of KM\overline{KM} is given as 2x52x - 5

Since the total length of KMKM is equal to the sum of KLKL and LMLM, we can set up the equation:

KM=KL+LMKM = KL + LM

Substitute the given values:

2x5=12+(x5)2x - 5 = 12 + (x - 5)

Now, solve for xx.

Step 1: Simplify the equation

2x5=12+x52x - 5 = 12 + x - 5 2x5=x+72x - 5 = x + 7

Step 2: Subtract xx from both sides

2xx=7+52x - x = 7 + 5 x=12x = 12

Step 3: Find the length of KMKM

Now that we have x=12x = 12, substitute it into the expression for KMKM:

KM=2x5=2(12)5=245=19KM = 2x - 5 = 2(12) - 5 = 24 - 5 = 19

Final Answer:

  • x=12x = 12
  • Length of KM=19\overline{KM} = 19

Would you like further details or have any questions?

Here are some related questions to consider:

  1. What if the total length KMKM was given in a different form?
  2. How would the problem change if LMLM had a different expression?
  3. How do you apply the segment addition postulate in different scenarios?
  4. What happens if we rearrange points KK, LL, and MM on the line?
  5. How would you handle this if it was a three-dimensional geometry problem?

Tip: When solving geometric problems, it's important to clearly identify the known values and the relationships between segments to set up the correct equations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Segment Addition Postulate

Formulas

Segment Addition Postulate: KM = KL + LM

Theorems

Segment Addition Postulate

Suitable Grade Level

Grades 8-10