Triangle Inequality

In other words, if you have a triangle with sides a, b, and c, then a + b > c, b + c > a, and c + a > b.

A step-by-step guide to Using Triangle Inequality Rules

For example, if you have a triangle with sides of lengths 4, 5, and 7, you can check whether it satisfies the triangle inequality:

• 4 + 5 > 7 (true)
• 5 + 7 > 4 (true)
• 7 + 4 > 5 (true)

Since all three conditions are true, this triangle satisfies the triangle inequality and is a valid triangle.

On the other hand, if you have sides of lengths 2, 5, and 10:

• 2 + 5 > 10 (false)
• 5 + 10 > 2 (true)
• 10 + 2 > 5 (true)

In this case, the first condition is false, which means that these side lengths do not form a valid triangle.

Triangle Inequality – Example 1

Do the given sides form a triangle? \(a=3, b=5, c=8\)
Solution:
Add the first and second lengths. \(3+5=8\)
8 is equal to the third length. So, it is not a triangle.

Triangle Inequality – Example 2

Do the given sides form a triangle? \(a=7, b=6, c=12\)
Solution:
Add the first and second lengths. \(7+6=13\)
13 is larger than the third length (12). So, they form a triangle.