Question

A square lawn is surrounded by a path 3m wide around it. if the area of the path is 180sq m find the area of lawn​

Answer 1

Answer:

812.25 cm^2

Step-by-step explanation:

(x + 3)^2 = 180 + x^2

x^2 + 9 + 6x = x^2 + 180

2x + 3 = 60

2x = 57

x=57/2

Area of lawn = x^2

= 57/2 * 57/2

=3249/4 = 812.25 cm^2

Answer 2

Step-by-step explanation:

Consider the side of the lawn be x

Given width of the path = 3m

Side of the lawn including path = x + 2(3m) = x + 6m

So, area of lawn =

(Area of the lawn including the path) - (Area of the path)

Area of a square = (side)*2

Therefore, we say :

x*2 = (x + 6)2 – 180m2

x*2 = (x*2 + 12x +36) - 180m2

x*2 = x*2+ 12x + 36 - 180

x*2 = x*2 + 12x - 144

x*2 - 144 = x*2 - 12x

x*2 - x2 - 144 = -12x

-144 = -12x

i.e 144 = 12x

Hope it will help you .