I have a triangle with sides of length 60, 80, and x. 
x is the lengthiest.
x is three times as long as the shortest side minus the 2nd lengthiest side.
How long is x?

Given the triangle with sides of lengths 60, 80, and \( x \), where \( x \) is the longest side, we are also given that \( x \) is three times the shortest side minus the second longest side. We need to find the value of \( x \).

First, identify the sides in terms of shortest to longest:
- Shortest side: 60
- Second longest side: 80
- Longest side: \( x \)

The relationship given is:
\[ x = 3 \times (\text{shortest side}) - (\text{second longest side}) \]

Substituting the given values:
\[ x = 3 \times 60 - 80 \]
\[ x = 180 - 80 \]
\[ x = 100 \]

Thus, the length of \( x \) is 100.

Let's verify this:
- Shortest side: 60
- Second longest side: 80
- Longest side: 100

The sides satisfy the triangle inequality theorem:
1. \( 60 + 80 > 100 \)
2. \( 60 + 100 > 80 \)
3. \( 80 + 100 > 60 \)

All the conditions hold true. Therefore, \( x = 100 \) is a valid solution.

Would you like more details or have any questions?

Here are 5 additional questions you might want to ask:
1. Can you explain the triangle inequality theorem in more detail?
2. How do you determine if three sides form a valid triangle?
3. What are the types of triangles based on their sides?
4. How do you calculate the area of a triangle given its sides?
5. What is the Pythagorean theorem and how does it apply to triangles?

**Tip:** When solving geometry problems, always check the conditions or theorems related to the shapes involved to ensure your solutions are valid.

Find out how to determine the length of the longest side in a triangle with sides of lengths 60, 80, and x, where x is three times the shortest side minus the second longest side. Understand the application of the triangle inequality theorem in solving this geometry problem. Suitable for Grades 7-9.

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