Q. 24.3( 7 Votes )

A square lawn is surrounded by a path 2.5 m wide. If area of the path is 165 m2, find the area of the lawn.

Answer :

Let ABCD be the square lawn of side ‘x’ m that is AB = x.


Given path is 2.5 m wide (shaded region).



So, side of square EFGH (lawn along with the path) as shown in the above figure is given by


EF = (x + 2.5 + 2.5) m


EF = (x + 5) m


We have area of lawn equal to the difference between the area of the lawn along with the path and the area of the path (shaded region).


area of ABCD = area of EFGH – area of the shaded region


We know, Area of a square = side2


So, we have Area of square ABCD = AB2


Area of ABCD = x2 m2


Similarly, we have Area of square EFGH = EF2


Area of EFGH = (x + 5)2 m2


Given area of the path = 165 m2


x2 = (x + 5)2 – 165


(x + 5)2 – x2 = 165


x2 + 10x + 25 – x2 = 165


10x + 25 = 165


10x = 140



So, side of the square lawn is 14 m.


Area of the square lawn = 142 = 196 m2


Thus, area of the lawn is 196 m2.


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