The sides of a rectangle are in the ratio 5 : 4 and its perimeter is 90 cm.

Let the length of two sides of the rectangle be $5 x \mathrm{~cm}$ and $4 x \mathrm{~cm}$, respectively.

Then, its perimeter $=2(5 x+4 x) \mathrm{cm}$

$=18 x \mathrm{~cm}$

$\therefore 18 x=90$

$\Rightarrow x=\frac{90}{18}$

$\Rightarrow x=5$

Length of one side $\Rightarrow(5 \times 5) \mathrm{cm}=25 \mathrm{~cm}$

Length of the other side $\Rightarrow(4 \times 5) \mathrm{cm}=20 \mathrm{~cm}$

$\therefore$ Length of the rectangle $=25 \mathrm{~cm}$

Breadth $=20 \mathrm{~cm}$