the length and the breadth of a rectangular Park are in the ratio 8 ratio 5.
A path 1.5 metre wide running all around the outside of a park has an area of 594 square. find the dimension of the park

Dear Student,

Solution)
​​​​​​Given: length and breadth of rectangular park in the ration 8:5
 let the length of park (l) =8x
then breadth (b) = 5x

So, area of park = 
                          = =8x×5x=40x^2

Also, width of path = 1.5 m (given)
outer length (L)=8x+2×1.5 = (8x+3)=8x+2×1.5 = (8x+3) m
and breadth (B) =5x+2×1.5 = (5x+3)=5x+2×1.5 = (5x+3)m

Area of path                       
​​​​=(8x+3)×(5x+3)−8x×5x
=40x^2 +24x+15x+9−40x^2
=(39x+9) m^2
 

Given that the area of path= 594 m²

Therefore,
(39x+9)=594        
39x=585           
​​​​​​x =15
​​​​​​
Hence, length of the park=8x=8×15=120m

And breadth of the park=5x=5×15=75 m

Regards!