Kyrie drew two triangles with the same perimeter. 
 
5x 5x 3x+2
 

What is the perimeter of each triangle?  Use the keypad to enter your answer.
 

Let's solve this problem step by step.

We are told that Kyrie drew two triangles with the same perimeter. One triangle has side lengths \( 5x \), \( 5x \), and \( 3x + 2 \).

### Step 1: Write the equation for the perimeter of the first triangle.

The perimeter of the first triangle can be found by adding the lengths of its three sides:

\[
\text{Perimeter}_1 = 5x + 5x + (3x + 2)
\]

Simplifying this:

\[
\text{Perimeter}_1 = 10x + 3x + 2 = 13x + 2
\]

### Step 2: The triangles have the same perimeter.

Since both triangles have the same perimeter, the perimeter of the second triangle must also be \( 13x + 2 \).

Thus, the perimeter of each triangle is \( 13x + 2 \).

If you know the value of \( x \), you can substitute it in to find the numerical value of the perimeter.

Do you have any questions about the solution? Let me know if you want more details. Here are some related questions for you to consider:

1. How would the problem change if the second triangle had different side lengths?
2. What would happen if the value of \( x \) were given as a specific number?
3. Could you draw other triangles with the same perimeter but different side lengths?
4. How would the perimeter be affected if the formula for one of the triangle sides changed?
5. Can two triangles with the same perimeter ever be identical?

**Tip:** Always double-check the values of your variables to ensure you have the correct perimeter for each shape!

Learn how to calculate the perimeter of triangles where side lengths are given by expressions involving x. Understand how to find the perimeter when side lengths include variables. Suitable for Grades 7-9 students studying geometry and perimeter calculation.

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