In a rectangular part of dimension …

It is given that the dimensions of the rectangular park is 50 m {tex}\times{/tex} 40 m.
{tex}\therefore{/tex} Area of the rectangular park = 50 {tex}\times{/tex} 40 = 2000 m²
Area of the grass surrounding the pond = 1184 m²
Now,
Area of the rectangular pond
= Area of the rectangular park − Area of the grass surrounding the rectangular pond
= 2000 − 1184
= 816 m²
Let the uniform width of the surrounding grass be y.
{tex}\therefore{/tex} Length of the rectangular pond = (50 − 2y) m
Breadth of the rectangular pond = (40 − 2y) m
Now,
Area of rectangular pond = 816 m²
{tex}\therefore{/tex} (50 − 2y) {tex}\times{/tex} (40 − 2y) = 816
{tex}\Rightarrow{/tex} 2000 − 80y − 100y + 4y² = 816
{tex}\Rightarrow{/tex} 4y² − 180y + 2000 − 816 = 0
{tex}\Rightarrow{/tex} 4y² − 180y + 1184 = 0
{tex}\Rightarrow{/tex} y² − 45y + 296 = 0
{tex}\Rightarrow{/tex} y² − 37y − 8y + 296 = 0
{tex}\Rightarrow{/tex} y(y − 37) − 8(y − 37) = 0
{tex}\Rightarrow{/tex} (y − 8)(y − 37) =  0
{tex}\Rightarrow{/tex} y − 8 = 0 or y − 37 = 0
{tex}\Rightarrow{/tex} y = 8 or y = 37
For y = 37,
Length of rectangular pond = 50 − 2 {tex}\times{/tex} 37 = −24 m, which is not possible
So, y {tex}\ne{/tex} 37
Therefore, y = 8.
When y = 8,
Length of the rectangular pond = 50 − 2 {tex}\times{/tex} 8 = 50 − 16 = 34 m
Breadth of the rectangular pond = 40 − 2 {tex}\times{/tex} 8 = 40 − 16 = 24 m.