The perimeter of the parallelogram is 40 dm, and two of its sides are 2: 3. Find the sides of the parallelogram.

Since a parallelogram is a quadrangle, the opposite sides of which are equal, then its perimeter is:
P = 2 * a + 2 * b,
where a and b are adjacent sides of the parallelogram.
Let x be the coefficient of proportionality, then we denote side a as 2 * x, and side b will be equal to 3 * x. Now we can write an equation with one unknown:
2 * 2 * x + 2 * 3 * x = 40.
Here are similar ones:
4 * x + 6 * x = 40;
10 * x = 40;
x = 40/10 (proportional);
x = 4.
Find the length of side a:
a = 2 * x = 2 * 4 = 8 (dm).
Find the length of side b:
b = 3 * x = 3 * 4 = 12 (dm).
Answer: a = 8 dm, b = 12 dm.