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The triangle \( \triangle JKL \) has two labeled sides: \( JK = 2x + 28 \) and \( KL = 9x + 7 \). 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:

\[
JK = KL
\]

### Step-by-Step Solution

1. **Set up the equation:**
   \[
   2x + 28 = 9x + 7
   \]

2. **Solve for \( x \):**
   Subtract \( 2x \) from both sides:
   \[
   28 = 7x + 7
   \]
   Subtract 7 from both sides:
   \[
   21 = 7x
   \]
   Divide by 7:
   \[
   x = 3
   \]

3. **Calculate \( KL \):**
   Substitute \( x = 3 \) into the expression for \( KL \):
   \[
   KL = 9x + 7 = 9(3) + 7 = 27 + 7 = 34
   \]

### Final Answer
The length of side \( KL \) is \( 34 \).

Would you like further details or have any questions?

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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.

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.

This page provides a step-by-step solution to find the length of side KL in an isosceles triangle JKL with side expressions JK = 2x + 28 and KL = 9x + 7. Learn how to solve for x and calculate the side length, covering key algebraic and geometric concepts suitable for Grades 8-10.

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