Question

A square lawn is surrounded by a path 2 m wide. If the area of the path is 240 meter square, find the area of the lawn.

Answer 1

Here is a similar problem
pls change the values and proceed the same procedure

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.