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: It helps determine whether three given lengths can form a valid triangle.

2. How Does the Calculator Work?

The calculator checks all three conditions of the 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 for the sides to form a valid triangle.

3. Importance of Triangle Inequality

Details: This fundamental geometric principle is essential in construction, engineering, and computer graphics to ensure valid triangular shapes.

4. Using the Calculator

Tips: Enter the lengths of all three sides in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What happens if two sides equal the third?
A: The theorem is not satisfied (a + b = c forms a degenerate triangle - a straight line).

Q2: Does this work for all types of triangles?
A: Yes, the theorem applies to scalene, isosceles, and equilateral triangles.

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

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

Q5: What about right triangles?
A: Right triangles must satisfy both the triangle inequality and the Pythagorean theorem.