Question

a square lawn has 2 metre width Path surrounding it if the area of path is 136 m square find the area of loan

Answer 1

Consider the side of the lawn be x
Given width of the path = 2m
Side of the lawn including path = x + 2(2m) = x + 4m
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 + 4)2 – 136 m2
x2 = (x2 + 8x +16) - 136m2
x2 = x2+ 8x + 16 - 136
x2 = x2 + 8x - 120
x2 - 120 = x2 - 8x
x2 - x2 - 120 = -8x
-120 = -8x
i.e 120= 8x
Therefore x = 120/8 = 15
Since the side of the lawn = 1 m
The area of the lawn = (15)2 or 225m2.

Answer 2

Answer:

Step-by-step explanation:

Consider the side of the lawn be x

Given width of the path = 2m

Side of the lawn including path = x + 2(2m) = x + 4m

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 + 4)2 – 136 m2

x2 = (x2 + 8x +16) - 136m2

x2 = x2+ 8x + 16 - 136

x2 = x2 + 8x - 120

x2 - 120 = x2 - 8x

x2 - x2 - 120 = -8x

-120 = -8x

i.e 120= 8x

Therefore x = 120/8 = 15

Since the side of the lawn = 1 m

The area of the lawn = (15)2 or 225m2