Let the lengths of the sides be x and y respectively. Then;
\(\frac{x}{y} = \frac{2}{3}\)
x=\(\frac{2}{3} y\)
We also know that x+y=50
Replacing value of x;
\(\frac{2}{3} y+y=50
\)\(2y+3y=150\)
5y=150
y=30
x=\(\frac{2}{3} *30\)
x=20
The length of the sides of parallelogram are 20cm and 30 cm.