A square lawn has 2m wide path surrounding it. If the area of the path is 136m², dind the area of the lawn.
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A square lawn has 2m wide path surrounding it. If the area of the path is 136m², dind the area of the lawn.
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Given :-
A square lawn has 2 m wide path surrounding it.
Area of the path = 136m²
To Find :-
The area of the lawn.
Analysis :-
Consider the side length of lawn as a variable.
The area of path is the difference between area of square path and area of lawn.
Then make an equation and get the value of the variable accordingly.
Solution :-
We know that,
Given that,
Area of outer square - Area of inner square = Area of the path
Let us consider the side of the lawn to be 'x'. Then, the side length of path is x + 4
As per the given info,
[tex]\sf (x+4)^{2}-(x)^{2}=136[/tex]
[tex]\sf x^{2}+16+8x-x^{2}=136[/tex]
[tex]\sf 8x=136-16[/tex]
[tex]\sf 8x=120[/tex]
Finding the value of x,
[tex]\sf x=\dfrac{120}{8}[/tex]
[tex]\sf x=15 \ cm[/tex]
Therefore, the length of lawn is 15 cm.
By the formula,
[tex]\underline{\boxed{\sf Area \ of \ square= Side \times Side}}[/tex]
Given that,
Side (s) = 15 cm
Substituting their values,
Area = 15²
Area = 225 cm²
Therefore, the area of the lawn is 225 cm².
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