Math Problem Statement

If JK = 10, KL = 6x, and JL = 11x, what is KL?

Solution

To solve for KLKL, we can use the Triangle Inequality Theorem. According to this problem, points JJ, KK, and LL form a straight line, meaning JK+KL=JLJK + KL = JL.

Given:

  • JK=10JK = 10,
  • KL=6xKL = 6x,
  • JL=11xJL = 11x.

Using the equation JK+KL=JLJK + KL = JL, we substitute the values:

10+6x=11x10 + 6x = 11x

Now, solve for xx:

10=11x6x10 = 11x - 6x 10=5x10 = 5x x=2x = 2

Now that we have x=2x = 2, substitute it back into KL=6xKL = 6x:

KL=6(2)=12KL = 6(2) = 12

Thus, KL=12KL = 12.

Would you like more details on this solution? Here are five related questions to expand your understanding:

  1. What is the Triangle Inequality Theorem and when is it used?
  2. If JLJL was given as 15x15x, how would that change the problem?
  3. What would happen if KL=7xKL = 7x instead of 6x6x?
  4. How do we determine if the points form a straight line versus a triangle?
  5. What are the properties of a straight line in geometry?

Tip: Always double-check the relationships between the line segments to confirm whether they form a straight line or a triangle.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Geometry

Formulas

JK + KL = JL

Theorems

Triangle Inequality Theorem

Suitable Grade Level

Grades 6-8