The sides of a rectangle are in the ratio 2 : 3,

Let the side be $x \mathrm{~cm}$ and $y \mathrm{~cm}$.

So, we have :

$2(x+y)=20$

Sides are in the ratio $2: 3$.

$\therefore y=\frac{3 x}{2}$

Putting the value of $y$ :

$2\left(x+\frac{3 x}{2}\right)=20$

$\frac{2 x+3 x}{2}=10$

$5 x=20$

$x=4$

$\therefore y=\frac{3 \times 4}{2}=6$

Thus, sides of the rectangle will be $4 \mathrm{~cm}$ and $6 \mathrm{~cm}$.

$\mathrm{ABCD}$ is the rectangle having side $s 4 \mathrm{~cm}$ and $6 \mathrm{~cm}$.