Problem 1. The perimeter of an isosceles triangle is $3 dm$. Calculate its leg $b$, if its base is a side of an equilateral triangle with a perimeter of $18 \mathrm{~cm}$.
Solution. The length of the side of an equilateral triangle with a perimeter of $18 \mathrm{~cm}$ is $18: 3=6 \mathrm{~cm}$. Therefore, the base of the isosceles triangle is $a=6 \mathrm{~cm}$. Now, if we denote the leg of the isosceles triangle by $b$, then its perimeter is $L=a+2 b$, and since $a=6 \mathrm{~cm}$ and $L=3 \mathrm{dm}=30 \mathrm{~cm}$, we get $30=6+2 b$, i.e., $b=(30-6): 2=12 \mathrm{~cm}$.