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 $9025\ cm^2$.

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Updated on: 10-Oct-2022

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