The sides of a rectangle are in the ratio 4 : 5.

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

So, we have :

$2(x+y)=90$

Sides are in the ratio $4: 5$.

$\therefore \quad y=\frac{5 x}{4}$

Putting the value of $y$ :

$2\left(x+\frac{5 x}{4}\right)=90$

$\frac{4 x+5 x}{4}=45$

$9 x=180$

$x=20$

$\therefore y=\frac{5 \times 20}{4}=25$

Thus, the sides of the rectangle will be $20 \mathrm{~cm}$ and $25 \mathrm{~cm}$.