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A square flowerbed is surrounded by a path 10 cm wide around it. If the area of the path is 2000 cm sq, find the area of the square flower bed.
Given:
A square flowerbed is surrounded by a path 10 cm wide around it.
The area of the path is 2000 cm sq.
To do:
We have to find the area of the square flower bed.
Solution:
We know that,
Area of a square of side $s$ is $s^2$.
Let the length of the square flower bed be $x$.
This implies,
Length of the square flower bed including the path $=(10+x)\ cm$.
Area of the square flower bed $=x^2\ cm^2$
Area of the square flower bed including the path $=(10+x)^2\ cm^2$
Area of the path $=$ Area of the square flower bed including the path $-$ Area of the square flower bed
$2000=(10+x)^2-x^2$
$2000=100+2(10)(x)+x^2-x^2$
$2000-100=20x$
$20x=1900$
$x=\frac{1900}{20}$
$x=95\ cm$
The area of the square flower bed $=(95)^2\ cm^2$
$=9025\ cm^2$
The area of the square flower bed is $9025\ cm^2$.