Question

In the centre of a rectangular lawn of dimensions 50m×40 m, a rectangular pond has to be

constructed, so that the area of the grass surrounding the pond would be 1184
.

Find the length and breadth of the pond.

Answer 1

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Solution:-

Dimensions = 50 m and 40 m

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

Area of the grass surrounding the pond = 1184 m²

So, the area of the pond = area of the lawn - area of the grass

= 2000 - 1184

Area of the pond = 816 m²

Let the width of around the pond be 'x' m 

Then, the length of the pond = (50 - 2x) m

and the breadth of the pond = (40 - 2x) m

Area of the pond = 816 m²

⇒ (50 - 2x) × (40 - 2x) = 816

2000 - 80x - 100x + 4x² = 816

4x² - 180x + 2000 - 816 = 0

4x² - 180x + 1184 = 0 

dividing it by 4 we get

x² - 45x + 296 = 0

 x² - 37x - 8x + 296 =0

x(x - 37) - 8(x - 37) = 0

(x - 37) (x - 8) = 0

x = 37 or x = 8

suppose if x = 37, then

the length of the pond will be 50 - 2*37

 50 - 74 = - 24m, which is not possible because length cannot be negative.

Therefore the length of the pond = 50 - 2*8

50 - 16 = 34 m

and 

Breadth of the pond = 40 - 2*8

40 - 16 = 24 m

Length = 34 m and breadth = 24 m