Question

The length and breadth of a rectangular park are in the ratio 5:2. A 2.5-m-wide path
running all around the outside of the park has an area of 305 m². Find the dimensions of
the park.
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Answer 1

If the area is 305 sq m then,

let the length of the rectangular park be 5x

∴ breadth will be 2x

so area= l*b

               5x*2x

            =10x²

width of the park all around the park=2.5m

∴lenght and breadth including path (5x+2.5 +2.5)m=(5x+5) and breadth of rectangular park=(2x+2.5+2.5)=(2x+5)

thus, area of the park=[(5x+2)(2x+5)-10x²]m²=(35x+25)m²

it is given that 35x +25 =305

⇒35x=280

x=8

thus the lenght of th park=5*8=40m and breadth of the park=2*8=16m