1. What is the Triangle Inequality Theorem?

Definition: The theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

Purpose: This calculator helps determine if three given lengths can form a valid triangle according to the triangle inequality theorem.

2. How Does the Calculator Work?

The calculator checks these three conditions:

Where:

• \( a \) — Length of side A (meters)
• \( b \) — Length of side B (meters)
• \( c \) — Length of side C (meters)

Explanation: All three conditions must be true for the lengths to form a valid triangle. If any condition fails, the sides cannot form a triangle.

3. Importance of Triangle Inequality

Details: This fundamental geometric principle ensures that three lengths can physically connect to form a closed shape. It's essential in construction, engineering, and computer graphics.

4. Using the Calculator

Tips: Enter the three side lengths in meters. All values must be positive numbers. The calculator will determine if they satisfy the triangle inequality conditions.

5. Frequently Asked Questions (FAQ)

Q1: What if two sides equal the third side?
A: If a + b = c (or any other combination), it forms a degenerate triangle (a straight line), which is not considered a valid triangle.

Q2: Does this work for all types of triangles?
A: Yes, the inequality applies to all triangles - scalene, isosceles, equilateral, right, acute, and obtuse.

Q3: What units should I use?
A: The calculator uses meters (m), but you can use any unit as long as all three sides use the same unit.

Q4: Can I use decimal values?
A: Yes, the calculator accepts decimal values for precise measurements.

Q5: What about negative lengths?
A: The calculator automatically rejects negative values as physical lengths cannot be negative.