Mathematics 8 Triangle Inequality Solutions and Explanations

To solve problems involving side lengths, start by verifying the condition for each set of values. The sum of the lengths of any two sides of a triangle must always be greater than the length of the third side. This is the foundation for determining if a set of values can form a valid triangle. Use this principle to eliminate impossible combinations and focus on valid ones.

For example, consider three lengths: 5, 7, and 12. Add the first two sides: 5 + 7 = 12. Since this sum equals the third side, these lengths cannot form a valid triangle. The sum must strictly be greater, not equal.

Make sure to check each condition individually: (Side 1 + Side 2 > Side 3), (Side 1 + Side 3 > Side 2), and (Side 2 + Side 3 > Side 1). This ensures that the relationship holds for every combination, confirming whether or not a valid shape can be formed.