Competition problem — Geometry — Maths Olympiad Prep

Library / /2 of 20

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. Spacing and $ signs are ignored.

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 $11$ .

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement and solution reproduced as published; topic and difficulty added by this site.