In the centre of a rectangular lawn of dimensions 50 m x 40 m, a rectangular pond has to be constructed, so that the area of the grass surrounding the pond would be 1184 m² [see figure]. Find the length and breadth of the pond.

Question

Philoid · Accepted 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 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

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

In the centre of a rectangular lawn of dimensions 50 m x 40 m, a rectangular pond has to be constructed, so that the area of the grass surrounding the pond would be 1184 m2 [see figure]. Find the length and breadth of the pond.