## Task 3 - 270713

In a triangle, the measurements of the lengths of all sides in centimeters are integers, even, and distinct from each other. It is known that $a=6 \mathrm{~cm}$ and $b=4 \mathrm{~cm}$.

Determine whether the perimeter of the triangle can be uniquely determined from these data! If this is the case, then give the perimeter!
In every triangle, one side is always smaller than the sum and always greater than the difference of the other two sides.

Consequently, according to the problem, $2 \mathrm{~cm}<c<10 \mathrm{~cm}$, where $c$ is the length of the third side of the considered triangle. Since, by assumption, the value of $c$ is even and different from 4 and 6, only $c=8$ $\mathrm{cm}$ satisfies all conditions.

The perimeter $u$ of the triangle can thus be determined uniquely, and it holds that: $u=6+4+8=18 \mathrm{~cm}$.