Triangle Inequality Calculator

Triangle Inequality

Check if 3 sides can form a triangle

How to Test Triangle Inequality

Step 1: Collect All Three Side Lengths

Measure or obtain the lengths of all three sides: A, B, and C.

Why: All three sides are needed. You cannot determine if three segments form a triangle without all measurements.

Step 2: Verify All Sides Are Positive

Check that A, B, and C are all greater than zero.

Why: Negative or zero lengths are impossible in real geometry. This catches invalid input immediately.

Step 3: Test First Inequality

Check that A + B > C (sum of two shortest sides exceeds the longest).

Why: If this fails, the other two checks will also fail. This is typically the most restrictive condition.

Step 4: Test Remaining Inequalities

Verify A + C > B and B + C > A (all three combinations must pass).

Why: The triangle inequality theorem requires ALL three conditions. Failure of any one means no triangle forms.

Step 5: Interpret the Result

Valid triangle means sides can physically connect. Invalid result means measurement error or intended non-triangle.

Why: This test is fundamental to geometry. Systems often use it to validate input before proceeding with further calculations.

Real-World Example

Validating Triangular Bracing

Scenario: An engineer has three rods measuring 5m, 7m, and 11m. Can they form a triangular brace?
Step 1: Sides collected: A = 5m, B = 7m, C = 11m
Step 2: All positive: 5 > 0 ✓, 7 > 0 ✓, 11 > 0 ✓
Step 3: Test 1: 5 + 7 = 12 > 11 ✓
Step 4: Test 2: 5 + 11 = 16 > 7 ✓; Test 3: 7 + 11 = 18 > 5 ✓
Step 5: Result: VALID TRIANGLE - all three tests passed
Verification: All inequalities satisfied; geometry is sound for bracing
Result: These rods form a valid triangle and can be used for brace construction
Interpretation: The engineer can proceed with assembly. If any test had failed, the design would need reworking with different rod lengths.

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