Question

A square flowerbed is surrounded by a path 10 cm wide around it. If the area of the path is 2000 cm${}^2$, find the area of the square flower-bed.

Answer 1

In the adjoining figure,

ABCD is the square flowerbed.

EFGH is the outer boundary of the path.

Let each side of the flowerbed = x cm

Then, the area of the square flowerbed ABCD $(x\times x)$ cm${}^2$ = x${}^2$ cm${}^2$

Now, the side of the square EFGH = (x+10+10) cm = (x+20) cm

So, the area of square EFGH =(x+20) (x+20) cm${}^2$=(x+20)${}^2$ cm${}^2$

Therefore, area of the path = Area of EFGH - Area of ABCD

$=[x+20{)}^2-x^2]$ cm ${}^2$

$=[x^2+400+40x-x^2]$ cm${}^2=(40x+400)$ cm${}^2$

But the area of path given = 2000 cm${}^2$

Therefore, 40x+400=2000

$\Rightarrow 40x=2000-400$

$\Rightarrow 40x=1600$

$\Rightarrow x=\frac{1600}{40}$

Therefore, side of square flowerbed = 40 cm

Therefore, the area of the square flowerbed $=40\times 40$ cm${}^2$