Question

The length and the breadth of 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 m2. Find the dimensions of the park.

Answer 1

Answer:

Hence, the dimensions of the park are 120 m x 75 m

Step-by-step explanation:

Hi,

Let the length of the park be 'l'

Let the breadth of the park be 'b'

Given that l : b = 8 : 5

=> l/b = 8/5

=> 5l = 8b---------------(1)

Given the width of running path , w = 1.5 m

From the diagram we can clearly observe that,

Area of running path outside the park

= Area of 4 corner squares each of side as running path width 'w'

+ Area of 2 rectangles of length as 'l' and breadth as 'w'

+ Area of 2 rectangles of length as 'b' and breadth as 'w'

=> 4w² + 2lw + 2bw = 594

=> 9 + 3(l + b) = 594

=> 3(l + b) = 585

=> l + b = 195

Using (1), we get

8b/5 + b = 195

=> 13b/5 = 195

=> b = 75 m

and l = 120 m

Hence, the dimensions of the park are 120 m x 75 m

Hope, it helps !