https://file.aiquickdraw.com/mathbot/file/1726621642360jcsb1e6v.jpg

The problem shows a triangle with sides labeled as 15 units, 15 units, and \(7x\) units, with a given perimeter of \(17x\) units.

### Steps to solve for \(x\):

1. **Perimeter formula for a triangle**: The perimeter is the sum of all sides.
   \[
   \text{Perimeter} = 15 + 15 + 7x
   \]

2. **Equating the given perimeter**: The problem states that the perimeter is \(17x\) units.
   \[
   15 + 15 + 7x = 17x
   \]

3. **Simplify the equation**:
   \[
   30 + 7x = 17x
   \]

4. **Solve for \(x\)**:
   Subtract \(7x\) from both sides:
   \[
   30 = 17x - 7x
   \]
   Simplify:
   \[
   30 = 10x
   \]

5. **Final value of \(x\)**:
   Divide both sides by 10:
   \[
   x = 3
   \]

Thus, the value of \(x\) is **3**.

Would you like more details or have any questions? 

Here are 5 related questions:
1. What is the length of the base of the triangle when \(x = 3\)?
2. What is the total perimeter of the triangle when \(x = 3\)?
3. How do we calculate the area of this triangle?
4. What type of triangle is this based on its side lengths?
5. How does the equation change if one side of the triangle is modified?

**Tip:** Always double-check units and simplify equations step by step to avoid mistakes!

The perimeter of the triangle is 17x units, with side lengths 15 units, 15 units, and 7x units. Write and solve an equation to find the value of x.

Learn how to solve a triangle perimeter equation where the perimeter is given as 17x units, and the side lengths are 15 units, 15 units, and 7x units. A step-by-step algebraic solution is provided, perfect for students in Grades 6-8.

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