Question

The length and the 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 5 9 4 m square . Find the dimension of park

Answer 1

Define x:

Given that the ratio of length and breadth = 8 : 5

Let the length of the park be 8x

And the breadth of the park be 5x


Find the area of the park in term of x:

Area = Length x Breadth

Area = (8x) x (5x)  = 40x² m²


Find the Length and Breadth of the park and the path:

Length = 8x + 1.5 + 1.5 =  ( 8x + 3 ) m²

Breadth = 5x + 1.5 + 1.5 = (5x + 3) m²


Find the area of the park and the path:

Area = Length x Breadth

Area = (8x + 3) (5x + 3)  m²


Solve x:

Given that the area of the path is 594 m²

(8x + 3) (5x + 3)  - 40x² = 594

40x² + 24x + 15x + 9 - 40x² = 594

39x + 9 = 594

39x = 585

x = 15 m


Find the dimension of the park:

Length = 8x = 8(15) = 120 m

Breadth = 5x = 5(15) = 75 m


Answer: The park is 120 m by 75 m