1.

A square lawn is surrounded by a path 2.5 m wide. If the area of the path is 165 m². findthe area of the lawn.​

Answer»

Question:

A SQUARE LAWN is surrounded by a path 2.5 m wide. If the area of the path is 165 m².Find  the area of the lawn.​

Given:

Width of the path = 2.5 m

Area of path = 165m²

To Find:

SIDE of the lawn

Formula USED:

  • S x S

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

Solution:

Let the side of the square lawn be x

Given width of the path = 2.5 m

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

=x+2 (2.5)

= x+5

Area of a square when side is given is S² or S x S

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

x^2=(x+5)^2-165\\\\x^2=(x^2+10x+25)-165\\\\x^2=x^2+10x+25-165\\\\x^2=x^2-140+10x\\\\x^2-x^2-140=-10x\\\\-140=-10x\\\\10x=140\\\\x=\frac{140}{10}\\\\=14 m

The area of the lawn=(14)² or 196 m²

Answer:

(14)² or 196 m²


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