Q. 74.1( 53 Votes )

In the centre of

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


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