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South African Mathematics Olympiad Second Round

South Africa geometry

Problem

The lengths of all sides of a triangle are prime numbers. If two sides are and what is the longest possible length of the third side?
Solution
The length of the third side of a triangle cannot exceed the sum of the lengths of the first two sides, which is . The largest prime number less than is .
Final answer
11

Techniques

Triangle inequalitiesTriangle inequalitiesPrime numbers