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Question

In a rectangular park of dimensions 50×40m,a rectangular pond is constructed so that the area of grass strip of uniform width surrounding the pond would be 1184 m2.Find the length an breadth of the pond.


Solution

Here we assume uniform width of grass strip = x
So, from given information we get

50×40(502x)(402x)=11842000(2000100x80x+4x2)=118420002000+18ox4x2=11844x2180x+1184=04(x245x+296)=0x245x+296=0x237x8x+296=0,

Here we use splitting the middle term method

x(x37)8(x37)=0(x8)(x37)=0Sox=8 and 37

At x =8 we get the dimension of the pond, As:

Length of pond =502x=502×8=5016=34 m

And

Breadth of pond =402x=402×8=4016=24 m

And at x = 37 we get dimension of pond , As:

Length of pond =502x=502×37=5074=24 m,

But we can't have negative dimension so we neglect value of x = 37 and get (As we calculated dimension by taking x = 8)

Length of pond = 34 m

And

Breadth of pond = 24 m

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