Answer
$15$ cm $\times$ $12$ cm
Work Step by Step
Let $x$ cm and $y$ cm be the length and width of the rectangle, respectively.
We have the system:
$xy=180$
$2x+2y=54$
Multiplying the second equation by $y$, we have
$xy=180$
$2xy+2y^2=54y$
Substituting the first equation to the second one, we have
$2\cdot 180+2y^2=54y$
$2y^2-54y+360=0$ $(\div 2)$
$y^2-27y+180=0$
$(y-12)(y-15)=0$
$y=12$ or $y=15$
If $y=12$, then $12x=180\to x=15$.
If $y=15$, then $15x=180\to x=12$.
So, the rectangle has the dimensions of $15$ cm $\times$ $12$ cm.
