Answer:
We know that the ratio of length and breadth of a rectangular playground is 3:2
Then if the length is L, and the breadth is B, we have the relationship:
L = (3/2)*B
Outside this playground, we have a jogging track of 2m, then if we also consider the jogging track the length and breadth are:
L' = L + 2m
B' = B + 2m
The area is the product between the area and the breadth, then the area is:
A = B'*L'
A = (L + 2m)*(B + 2m)
And remember that L = (3/2)*B
Then we get:
A = ((3/2)*B + 2m)*(B + 2m)
And the area is 2816 m^2
Then we have:
A = ((3/2)*B + 2m)*(B + 2m) = 2816 m^2
Now we can solve the equation:
((3/2)*B + 2m)*(B + 2m) = 2816 m^2
(3/2)*B^2 + 3m*B + 2m*B + 4m^2 = 2816 m^2
(3/2)*B^2 + 5m*B = 2816 m^2 - 4m^2 = 2812m^2
Then we can write:
(3/2)*B^2 + 5m*B - 2812m^2 = 0
We can solve this if we use Bhaskara's formula:
One solution is negative, so we can discard that one, then we only take the positive:
B = (-5m + 130m)/3 = 41.67m
And L = (3/2)*B
L = (3/2)*40.7m = 62.5m
The breadth is 41.67 meters and the length is 62.5 meters.