# In the centre of

Let the distance between the pond and the rectangular lawn from all sides be x m.

Let the length of the rectangular pond be l m

l = (50 - 2x) m

Let the breadth of the rectangular pond be b m

b = (40 - 2x) m

Given,

Area of the grass surrounding the pond = 1184 m2

Area of the rectangular lawn,

= (l * b) = (50m * 40m) = 2000 m2

Area of the rectangular pond,

= (l * b) = (50 - 2x) (40 - 2x) m2

According to question,

2000 - (50 - 2x) (40 - 2x) = 1184

2000 - (2000 - 80x - 100x + 4x2) = 1184

4x2 - 180x + 1184 = 0

x2 - 45x + 296 = 0    For x = 37, Length and breadth of the pond will be −24m and −34m respectively. Hence, length and breadth cannot be negative. (Not possible)

Length of the pond = (50 - 2x) = 34m

Breadth of the pond = (40 - 2x) = 24m

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