From statement I, If the length = x metre and breadth = y metre, then y =
1×2
4
(x + y) ⇒ 2y = x + y ⇒ y = x ∴ x2 = 144 ⇒ x = √144 = 12 metre Area of field (16)2−(12)2 = 256 - 144 = 112 sq. metre From statement II and III. Length = 3x metre Breadth = 2x metre ∴ 3x × 2x = 216 ⇒ x2 =
216
3×2
= 36 ⇒ x = 6 ∴ Length = 18 metre, Breadth = 12 metre Area of the field with boundary = (18 + 2 × 2) (12 + 2 × 2) = 22 × 16 = 352 sq. m ∴ Area of boundary = 352 – 216 = 136 sq. m