Math Problem Statement

Find the length of the indicated side KL in the triangle JKL where JK = 2x + 28 and KL = 9x + 7, assuming it is an isosceles triangle.

Solution

The triangle JKL\triangle JKL has two labeled sides: JK=2x+28JK = 2x + 28 and KL=9x+7KL = 9x + 7. Given that the triangle is marked as isosceles (indicated by the two red tick marks), we can assume that the two sides with these markings are equal. Therefore:

JK=KLJK = KL

Step-by-Step Solution

  1. Set up the equation: 2x+28=9x+72x + 28 = 9x + 7

  2. Solve for xx: Subtract 2x2x from both sides: 28=7x+728 = 7x + 7 Subtract 7 from both sides: 21=7x21 = 7x Divide by 7: x=3x = 3

  3. Calculate KLKL: Substitute x=3x = 3 into the expression for KLKL: KL=9x+7=9(3)+7=27+7=34KL = 9x + 7 = 9(3) + 7 = 27 + 7 = 34

Final Answer

The length of side KLKL is 3434.

Would you like further details or have any questions?


Here are 5 related questions to expand on this concept:

  1. How do you determine if a triangle is isosceles based on given side lengths or angle properties?
  2. What are the steps to solve for a variable in similar geometric situations?
  3. How can we verify if a triangle is isosceles when given angle measures instead of side lengths?
  4. How would the approach change if the triangle were scalene instead of isosceles?
  5. How can you use properties of isosceles triangles to find missing angles?

Tip: Remember, in an isosceles triangle, the two equal sides are opposite the two equal angles, which can help in identifying congruent parts.

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Isosceles Triangle Properties

Formulas

Setting two expressions equal to solve for a variable

Theorems

Isosceles Triangle Theorem

Suitable Grade Level

Grades 8-10