# a square lawn is surrounded by a path of 2.5 m wide . if the area of the path is 165m2 find the area of the lawn ??

Let the side of the lawn be x

Since the width of the path = 2.5m

Side of the lawn including path = x + 2(2.5m) = x + 5m

So, area of lawn = (Area of the lawn inculding the path) - (Area of the path)

We know that the area of a square = (side)^2

Therefore, we say :

x^2 = (x + 5)^2 - (165^m.sq)

x^2 = (x^2 + 5x +5x +25) - (165m.sq)

x^2 = x^2 + 10x + 25 - 165

x^2 = x^2 + 10x - 140

x^2 - 140 = x^2 - 10x  (By transposing off)

x^2 - x^2 - 140 = -10x  (By transposing off)

-140 = -10x

i.e 140 = 10x

Therefore x = 140/10 = 14

Since the side of the lawn = 14m

The area of the lawn = (14)^2 or 196m.sq.

• 6

Let the side of the lawn be x

Since the width of the path = 2.5m

Side of the lawn including path = x + 2(2.5m) = x + 5m

So, area of lawn = (Area of the lawn inculding the path) - (Area of the path)

We know that the area of a square = (side)^2

Therefore, we say :

x^2 = (x + 5)^2 - (165^m.sq)

x^2 = (x^2 + 5x +5x +25) - (165m.sq)

x^2 = x^2 + 10x + 25 - 165

x^2 = x^2 + 10x - 140

x^2 - 140 = x^2 - 10x

x^2 - x^2 - 140 = -10x

-140 = -10x

i.e 140 = 10x

Therefore x = 140/10 = 14

Since the side of the lawn = 14m

The area of  lawn = (14)^2 or 196m.sq.

• 3

Yes, Kaushtubh is correct.

• 3
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