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In the adjoining figure, ABCD is a square grassy lawn of area $729m^2$. A path of uniform width runs all around it. If the area of the path is $295 m^{2}$, find
(i) the length of the boundary of the square field enclosing the lawn and the path.
(ii) the width of the path.
"
Given :
Area of the square ABCD $= 729 m^2$ .
Area of the path $= 295 m^2$
To find :
We have to find
(i) the length of the boundary of the square field enclosing the lawn and the path.
(ii) the width of the path.
Solution :
Let the length of the side of the square ABCD be x.
This implies,
$x^2=729 m^2$
$x^2 = 27\times27 m^2 $
$x = 27 m$.
A path of uniform width runs around the lawn.
Area of the path $= 295 m^2$
Let the width of the path be w.
This implies,
The length of the bigger square $= 27+w$ m.
Area of the bigger square $= Area of the lawn + Area of the path$
$= (729+295) m^2$
$= 1024 m^2$
Area of the bigger square $= (27+w)^2 m^2$
$1024 = (27+w)^2$
$32\times32 = (27+w)^2$
$(27+w) = 32$
$w = 32-27$
$w = 5$ m.
The width of the path is 5 m.
The length of the boundary of the square field enclosing the lawn and the path is $(27+5) m = 32 m$.
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