Area of rectangular field is 3584 m 2 and the length and the breadth are in the ratio 7 : 2, respectively. What is the perimeter of the rectangle?

Let length of the rectangular field = 7k m
and breadth of the rectangular field = 2k m
According to the question,
Area of a rectangular field = Length x Breadth
⇒ 3584 = 7k x 2k
⇒ 14 x k² = 3584
⇒ k² = 3584/14 = 256
⇒ k² = 256 = 16 m
∴ Length of rectangular field = 7k = 7 x 16 = 112 m
And breadth of rectangular field = 2 x 16 = 32 m
∴ Perimeter of rectangle = 2(Length x Breadth)
= 2(112 + 32)
= 2 x 144
= 288 m