## Task 5 - 140735

The perimeter of a triangle with side lengths $a, b, c$ is $34 \mathrm{~cm}$. Furthermore, $a: b=3: 8$ and $b: c=4: 3$.

Determine the side lengths!
It is given that $a: b=3: 8, b: c=8: 6$ (extension of $4: 3$ by 2), from which it follows that $a: b: c=3: 8: 6$, i.e., $a, b$ and $c$ are, in sequence, the 3-, 8-, and 6-fold of the same length.

Since $3+8+6=17$ and given the perimeter of $34 \mathrm{~cm}$, this length is $2 \mathrm{~cm}$. Therefore, the sought side lengths are $a=6 \mathrm{~cm}, b=16 \mathrm{~cm}, c=12 \mathrm{~cm}$.