Question

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

Answer 1

Given, dimensions of rectangular lawn = 50 m × 40 m

Now, Area of the rectangular lawn = 50 × 40 = 2000 m2

Area of the grass surrounding the pond = 1184 m2

Therefore,  area of the rectangular pond = Area of the rectangular lawn - Area of the grass surrounding the pond = 2000 - 1184 = 816 m2

Let the width of the surrounding grass be x.

Therefore, length of rectangular pond = 50 - 2x 

and breadth of rectangular pond = 40 - 2x

Again, area of rectangular pond = 816

⇒ (50 - 2x)×(40 - 2x) = 816

⇒ 2000 - 80x - 100x + 4x2 = 816

⇒ 4x2 - 180x + 2000 - 816 = 0

⇒ 4x2 - 180x + 1184 = 0

⇒ x2 - 45x + 296 = 0

⇒ x2 - 37x - 8x + 296 = 0

⇒ x(x-37) - 8(x-37)= 0

⇒ (x-8)(x-37)= 0

⇒ x = 8 or 37

Now, x ≠ 37, because for x  = 37,

length of rectangular pond = 50 - 2(37) = -24 m which isn't possible.

Therefore, length of rectangular pond = 50 - 2(8) = 34 m 

and breadth of rectangular pond = 40 - 2(8) = 24 m

hope it helps!