# 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.

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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.