Let length of rectangular base = $$3x$$ cm and breadth = $$2x$$ cm Surface area of rectangular prism = $$2(lb+bh+hl)$$ => $$2[(3x imes2x)+(2x imes12)+(12 imes3x)]=288$$ => $$6x^2+24x+36x=frac{288}{2}=144$$ => $$x^2+10x-24=0$$ => $$x^2+12x-2x-24=0$$ => $$x(x+12)-2(x+12)=0$$ => $$(x-2)(x+12)=0$$ => $$x=-12,2$$ $$ecause x$$ cannot be negative, => $$x=2$$ Thus, length = $$3 imes2=6$$ cm and breadth = $$4$$ cm $$ herefore$$ Volume = $$lbh$$ = $$6 imes4 imes12=288$$ $$cm^3$$ => Ans - (A)