$\text{ABCD}$  is a rectangle. If the shaded area is $48c{m}^2$  and $AB:BC=3:2$ , then

the perimeter of the rectangle is

Area of shaded region $=\frac{1}{2}\times \text{area}\text{of}ABCD\text{rectangle}$

$48c{m}^2=\frac{1}{2}\times AB\times BC$

$\Rightarrow 48=\frac{1}{2}\times 3x\times 2x$

$\Rightarrow 48=3x^2$

$\Rightarrow x^2=16$

$\Rightarrow x=4cm$

$\therefore$  perimeter of rectangle $ABCD$

$=2\left(3x+2x\right)$

$=10x$

$=10\times 4$

$=40cm$