Let length of rectangular base = 3x cm and breadth = 2x cm Surface area of rectangular prism = 2(lb+bh+hl) ⇒ 2[(3x×2x)+(2x×12)+(12×3x)]=288 ⇒ 6x2+24x+36x=
288
2
=144 ⇒ x2+10x−24=0 ⇒ x2+12x−2x−24=0 ⇒ x(x+12)−2(x+12)=0 ⇒ (x−2)(x+12)=0 ⇒ x=−12,2 ∵ x cannot be negative ⇒ x = 2 Thus, length = 3 × 2 = 6 cm and breadth = 4 cm ∴ Volume = lbh = 6×4×12=288cm3