Answer :

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 m^{2}

Area of the rectangular lawn,

= (l * b) = (50m * 40m) = 2000 m^{2}

Area of the rectangular pond,

= (l * b) = (50 - 2x) (40 - 2x) m^{2}

According to question,

⇒ 2000 - (50 - 2x) (40 - 2x) = 1184

⇒ 2000 - (2000 - 80x - 100x + 4x^{2}) = 1184

⇒ 4x^{2} - 180x + 1184 = 0

**∴** x^{2} - 45x + 296 = 0

Using the quadratic formula,

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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