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South African Mathematics Olympiad Second Round

Geometry Difficulty 3.6 AMC 10/12 Find the answer South Africa

The lengths of all sides of a triangle are prime numbers. If two sides are $5$ and $7$ what is the longest possible length of the third side?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

The length of the third side of a triangle cannot exceed the sum of the lengths of the first two sides, which is $5 + 7 = 12$ . The largest prime number less than $12$ is $11$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.