From statement I, if length = x m breadth = y m, then y =
1×2
4
(x+y) ⇒ 2y = x + y ⇒ y = x ∴ x2 =144 x = 144 = 12 m Area of field = (16)2–(12)2 = 256 –144 = 112 m2 From statement II and III, Length = 3x m Breadth = 2x m Area of rectangular field = 216 ∴ 3x × 2x = 216 ⇒
316
6
= 36 x = 6 ∴ Length = 18 m Breadth = 12 m Area of the field with boundary = (18+2 × 2)(12 + 2 × 2) = 22 ×16 = 352 m2 ∴ Area of boundary = 352-216 = 136 m2 Hence, statement I or statement II and III are sufficient to answer the question.