The sides of a rectangle are in the ratio 4 : 5 and its perimeter is 180 cm.

Let the length be $4 x \mathrm{~cm}$ and the breadth be $5 x \mathrm{~cm}$.

Perimeter of the rectangle $=180 \mathrm{~cm}$

Perimeter of the rectangle $=2(l+b)$

$2(l+b)=180$

$\Rightarrow 2(4 x+5 x)=180$

$\Rightarrow 2(9 x)=180$

$\Rightarrow 18 x=180$

$\Rightarrow x=10$

$\therefore$ Length $=4 x \mathrm{~cm}=4 \times 10=40 \mathrm{~cm}$

Breadth $=5 x \mathrm{~cm}=5 \times 10=50 \mathrm{~cm}$