Question

4. A square lawn is surrounded by a 3 metre wide path around it. If the area of the path is 180 m, find the area of the lawn.​

Answer 1

Answer:

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

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