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Question

A square flowerbed is surrounded by a path 10 cm wide around it. If the area of the path is 2000 cm2, find the area of the square flower-bed.

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Solution

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×x) cm2 = x2 cm2

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

So, the area of square EFGH =(x+20) (x+20) cm2=(x+20)2 cm2

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

=[x+20)2x2] cm 2

=[x2+400+40xx2] cm2=(40x+400) cm2

But the area of path given = 2000 cm2

Therefore, 40x+400=2000

40x=2000400

40x=1600

x=160040

Therefore, side of square flowerbed = 40 cm

Therefore, the area of the square flowerbed =40×40 cm2



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