Question

the length and breadth of a garden are in the ratio 2 : 1. a path and its perimeter is 240 m. a path of 2 m wide runs inside the garden along the boundary. find the area of the path

Answer 1

let the length and breadth of the park be 2x and x respectively.

Perimeter of the park = 240 m

2(2x+x) = 240

6x = 240

x = 40

So, length = 2×40 = 80 m

breadth = 40 m.

area of park = l×b = 80m×40m = 3200 m^2

Width of path = 2m

So, inner length = 80m -(2+2)m = 76m

inner breadth = 40 m -(2+2) = 36 m

area of inner part = inner l × inner b

= 76m × 36m = 2736 m^2

ar. of path = ar. of park - area of inner park

= (3200-2736) m^2 = 464 m^2