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  • 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 [see Fig. 4.1]. Find the length and breadth of the pond.

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.

Answers (1)

length = 34m, breadth = 24m

Let the distance between the pond and the loan boundary be x.

Hence the length of the pond =50-x-x

Then the breadth of the pond =40-x-x

From the figure

Area of lawn = Area of pond + Area of grass

50 × 40=(50-2x)(40-2x)+1184     (using Area of rectangle = l × B)

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

4x2-180x+2000-2000+1184=0

4x2-180x+1184=0

Divide by 4

x2-45x+296=0

x2 - 37x - 8x + 296 = 0

x(x-37)-8(x-37)=0

(x-37)(x-8)=0

x = 37, 8

If x = 37

Length of pond =50-2(37)

                        =50-74

                        =-24

Which is not possible because length can’t be negative.

If x = 8

Length of pond =50-2(8)

                        =50-16=34m

Breadth of pond =40-2(8)

                        =40-16=24m

Posted by

infoexpert24

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