The length and breadth of a rectangular park are in the ratio 8 : 5. A path, 1.5 m wide, running all around the outside of the park has an area of `594 m^(2)`. Find the dimensions of the park.

Explanation

Let the length and breadth of the park be 8x metres and 5x metres respectively.
Area of the park `=(8x xx 5x)m^(2)`
`=(40x^(2))m^(2)`.
Length of the park including the path = (8x + 3)m.
Breadth of the park including the path = (5x + 3)m.
Area of the park including the path `=(8x + 3)(5x + 3)m^(2)`
Area of the path `={(8x + 3)(5x + 3)-40x^(2)}m^(2) = (39x + 9)m^(2)`.
But, area of the path = 594 `m^(2)` ( given)
`therefore" "39x + 9 = 594 rArr 39x = 585`
`rArr x=(585)/(39)=15`.
`therefore" ""length of the park"= (8 xx 15)m = 120m`
and breadth of the park `= (5 xx 15)m = 75m`.