1. What is the Triangle Inequality Theorem?

Definition: The Triangle Inequality Theorem states that for any three lengths to form a triangle, the sum of any two sides must be greater than the third side.

Purpose: This calculator helps determine if three given lengths can form a valid triangle, which is fundamental in geometry, construction, and design.

2. How Does the Calculator Work?

The calculator checks all three conditions of the Triangle Inequality Theorem:

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 simultaneously for the lengths to form a valid triangle.

3. Importance of Triangle Validation

Details: Validating triangle side lengths is crucial in construction, engineering, and design to ensure structural integrity and feasibility of projects.

4. Using the Calculator

Tips: Enter all three side lengths in meters. The calculator will verify if they satisfy the triangle inequality conditions.

5. Frequently Asked Questions (FAQ)

Q1: What if two sides equal the third?
A: If a + b = c (or any 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 theorem applies to all triangles - scalene, isosceles, and equilateral.

Q3: What units should I use?
A: The calculator uses meters, but the theorem works with any consistent unit of measurement.

Q4: Can I use this for 3D triangles?
A: This calculator is for 2D triangles. 3D triangles (in space) have additional considerations.

Q5: What about negative or zero lengths?
A: Triangle sides must be positive numbers. The calculator will reject zero or negative values.