Base of a right prism is a rectangle, the ratio of whose length and breadth is 3 : 2. If the height of the prism is 12 cm and total surface area is 288 sq.cm, the volume of the prism is

Let length of rectangular base = $$3x$$ cm and breadth = $$2x$$ cm

Surface area of rectangular prism = $$2(lb+bh+hl)$$

=> $$2[(3x\times2x)+(2x\times12)+(12\times3x)]=288$$

=> $$6x^2+24x+36x=\frac{288}{2}=144$$

=> $$x^2+10x-24=0$$

=> $$x^2+12x-2x-24=0$$

=> $$x(x+12)-2(x+12)=0$$

=> $$(x-2)(x+12)=0$$

=> $$x=-12,2$$

$$\because x$$ cannot be negative, => $$x=2$$

Thus, length = $$3\times2=6$$ cm and breadth = $$4$$ cm

$$\therefore$$ Volume = $$lbh$$

= $$6\times4\times12=288$$ $$cm^3$$

=> Ans - (A)