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Do The Following Lengths Form A Triangle Calculator

Reviewed by Calculator Editorial Team

Determine whether three given lengths can form a valid triangle using our free online calculator. This tool applies the triangle inequality theorem to check the validity of your measurements.

How to Use This Calculator

To check if three lengths can form a triangle:

  1. Enter the three lengths in the input fields provided.
  2. Click the "Calculate" button to process the values.
  3. View the result which will indicate whether the lengths form a valid triangle.
  4. For invalid triangles, the calculator will explain which condition failed.

The calculator uses the triangle inequality theorem which states that for any three lengths to form a triangle, the sum of any two lengths must be greater than the third length.

Triangle Inequality Theorem

The triangle inequality theorem is a fundamental principle in geometry that defines the conditions under which three lengths can form a valid triangle. The theorem states:

For any three lengths a, b, and c to form a triangle, the following must be true:

  1. a + b > c
  2. a + c > b
  3. b + c > a

If all three conditions are satisfied, the lengths can form a triangle. If any one of these conditions fails, the lengths cannot form a triangle.

This theorem is essential for understanding the geometric constraints that apply to any set of three lengths that might potentially form a triangle.

Examples

Valid Triangle Example

Consider lengths 3, 4, and 5:

  • 3 + 4 > 5 → 7 > 5 (True)
  • 3 + 5 > 4 → 8 > 4 (True)
  • 4 + 5 > 3 → 9 > 3 (True)

All conditions are satisfied, so these lengths can form a valid triangle.

Invalid Triangle Example

Consider lengths 1, 2, and 4:

  • 1 + 2 > 4 → 3 > 4 (False)
  • 1 + 4 > 2 → 5 > 2 (True)
  • 2 + 4 > 1 → 6 > 1 (True)

Since one condition fails, these lengths cannot form a triangle.

Frequently Asked Questions

What is the triangle inequality theorem?
The triangle inequality theorem states that for any three lengths to form a triangle, the sum of any two lengths must be greater than the third length.
How do I know if three lengths can form a triangle?
Use our calculator to check the three conditions: a + b > c, a + c > b, and b + c > a. If all conditions are met, the lengths can form a triangle.
What happens if one condition fails?
If any one of the three conditions fails, the lengths cannot form a triangle. The calculator will indicate which condition failed.
Can I use negative numbers in the calculator?
No, lengths cannot be negative. The calculator will prompt you to enter positive values if you try to use negative numbers.
What if all three lengths are equal?
If all three lengths are equal, they will always form an equilateral triangle, which satisfies all conditions of the triangle inequality theorem.