Question

A square lawn is surrounded by a 5m wide path . If the area of the path is 400m², find the area of the lawn.
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Answer 1

Answer:

The area of the lawn is 196 meter square.

Step-by-step explanation:

Given : A square lawn is surrounded by a path 5 m wide. If the area of the path is 400 m square.

To find : The area of lawn ?

Solution :

Let the side of the lawn be x .

Width of the path = 5 m

Side of the lawn including path is x+2(5)=x+10

\text{Area of a square} = (side)^2Area of a square=(side)

2

Area of lawn = Area of the lawn including the path - Area of the path

i.e. x^2=(x+5)^2-165x

2

=(x+5)

2

−165

x^2=x^2+25+10x-165x

2

=x

2

+25+10x−165

10x=14010x=140

x=\frac{140}{10}x=

10

140

x=14x=14

The side of the lawn = 14 m

The area of the lawn is given by,

\text{Area of a lawn} = (14)^2Area of a lawn=(14)

2

\text{Area of a lawn} =196\ m^2Area of a lawn=196 m

2

Therefore, the area of the lawn is 196 meter square.