The area of a rectangle is 192 cm2 and its perimeter is 56 cm.

Solution:

Area of the rectangle = 192 cm2
Perimeter of the rectangle = 56 cm

Perimeter $=2$ (length $+$ breadth $)$

$\Rightarrow 56=2(l+b)$

$\Rightarrow l+b=28$

$\Rightarrow l=28-b$

Area $=$ length $\times$ breadth

$\Rightarrow 192=(28-b) x b$

$\Rightarrow 192=28 b-b^{2}$

$\Rightarrow b^{2}-28 b+192=0$

$\Rightarrow(b-16)(b-12)=0$

$\Rightarrow b=16$ or 12

Thus, we have;

$l=28-b$

$\Rightarrow l=28-12$

$\Rightarrow l=16$

We will take length as 16 cm and breath as 12 cm because length is greater than breadth by convention.