## Task 3 - 270723

The measures of two side lengths of a triangle are $a=12$ and $b=8$.

Determine all those numbers that can occur as the measure $c$ of the third side of the triangle so that the measure of the perimeter is a prime number. All three side lengths should be measured in the same unit, for example, in centimeters.
A number is a possible measure $c$ of the third side of a triangle if and only if it satisfies $ca-b$, i.e., $4<c<20$.

For the perimeter $u=a+b+c=20+c$ (1), this is equivalent to $24<u<40$.

This is a prime number if and only if $u$ is one of the numbers 29, 31, 37, and this, due to (1), is exactly when $c$ is one of the numbers $9,11,17$.