In a rectangular park of dimensions $50 \times 40 m$ ,a rectangular pond is constructed so that the area of grass strip of uniform width surrounding the pond would be 1184 $m^{2}$ .Find the length an breadth of the pond.

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Solution

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

$50 \times 40 - (50 - 2 x) (40 - 2 x) = 1184 \Rightarrow 2000 - (2000 - 100 x - 80 x + 4 x^{2}) = 1184 \Rightarrow 2000 - 2000 + 18 o x - 4 x 2 = 1184 \Rightarrow 4 x^{2} - 180 x + 1184 = 0 \Rightarrow 4 (x^{2} - 45 x + 296) = 0 \Rightarrow x^{2} - 45 x + 296 = 0 \Rightarrow x^{2} - 37 x - 8 x + 296 = 0,$

Here we use splitting the middle term method

$\Rightarrow x (x - 37) - 8 (x - 37) = 0 \Rightarrow (x - 8) (x - 37) = 0 S o \Rightarrow x = 8 a n d 37$

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

Length of pond $= 50 - 2 x = 50 - 2 \times 8 = 50 - 16 = 34 m$

And

Breadth of pond $= 40 - 2 x = 40 - 2 \times 8 = 40 - 16 = 24 m$

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

Length of pond $= 50 - 2 x = 50 - 2 \times 37 = 50 - 74 = - 24 m$ ,

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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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.

In a rectangular park of dimensions $50 \times 40 m$ ,a rectangular pond is constructed so that the area of grass strip of uniform width surrounding the pond would be 1184 $m^{2}$ .Find the length an breadth of the pond.