Question

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

Answer 1

Consider the side of the lawn be x
Given 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 including the path) - (Area of the path)
Area of a square = (side)2
Therefore, we say :
x2 = (x + 5)2 – 165 m2
x2 = (x2 + 10x +25) - 165m2

Answer 2

Let the side of the lawn be x

Given width of the path = 2.5m

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

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

Area of a square = (side)2

Therefore, we say :

x2 = (x + 5)2 – 165 m2

x2 = (x2 + 10x +25) - 165m2

x2 = x2+ 10x + 25 - 165

x2 = x2 + 10x - 140

x2 - 140 = x2 - 10x

x2 - x2 - 140 = -10x

-140 = -10x

i.e 140 = 10x

Therefore x = 140/10 = 14

Since the side of the lawn = 14 m

The area of the lawn = (14)2 or 196 m2.