Triangle Inequality Checker

Triangles are fundamental geometric shapes with many applications in fields ranging from computer graphics to structural engineering. A key property of triangles is the "triangle inequality theorem," which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This challenge requires you to implement a function that verifies if three given lengths can form a valid triangle.

Problem Description

Your task is to create a function that takes three positive numbers, representing the lengths of three potential sides of a triangle, and determines if these lengths can form a valid triangle.

Requirements:

• The function should accept three numerical inputs.
• The function should return a boolean value: true if the lengths can form a triangle, and false otherwise.
• The triangle inequality theorem must be applied: for sides A, B, and C, the following must all be true:
  • A + B > C
  • A + C > B
  • B + C > A
• All input lengths are assumed to be positive.

Expected Behavior:

• If all three conditions of the triangle inequality theorem are met, the function should return true.
• If any of the conditions are not met, the function should return false.

Edge Cases:

• Consider cases where two sides sum up to exactly the length of the third side (e.g., 3, 4, 7). This should result in false as it forms a degenerate triangle (a straight line).
• The problem statement guarantees positive inputs, so you do not need to explicitly check for zero or negative lengths.

Examples

Example 1:

Input: side1 = 3, side2 = 4, side3 = 5
Output: true
Explanation:
3 + 4 > 5 (7 > 5) - True
3 + 5 > 4 (8 > 4) - True
4 + 5 > 3 (9 > 3) - True
All conditions are met.

Example 2:

Input: side1 = 1, side2 = 2, side3 = 5
Output: false
Explanation:
1 + 2 > 5 (3 > 5) - False
Since one condition is false, the lengths cannot form a triangle.

Example 3:

Input: side1 = 7, side2 = 10, side3 = 5
Output: true
Explanation:
7 + 10 > 5 (17 > 5) - True
7 + 5 > 10 (12 > 10) - True
10 + 5 > 7 (15 > 7) - True
All conditions are met.

Example 4: (Edge Case)

Input: side1 = 2, side2 = 3, side3 = 5
Output: false
Explanation:
2 + 3 > 5 (5 > 5) - False
This represents a degenerate triangle (a straight line), which is not considered a valid triangle in this context.

Constraints

• The input side lengths will be positive integers.
• The maximum value for any side length will be 1000.
• The function should execute efficiently and complete within typical time limits for competitive programming or standard application development.

Notes

• Focus on correctly implementing the triangle inequality theorem.
• Pseudocode is provided for reference, but you should implement the solution in your preferred programming language.

Pseudocode:

FUNCTION canFormTriangle(side1, side2, side3):
  IF (side1 + side2 > side3) AND (side1 + side3 > side2) AND (side2 + side3 > side1):
    RETURN true
  ELSE:
    RETURN false
  END IF
END FUNCTION