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−(50−2x)(40−2x)=1184⇒2000−(2000−100x−80x+4x2)=1184⇒2000−2000+18ox−4x2=1184⇒4x2−180x+1184=0⇒4(x2−45x+296)=0⇒x2−45x+296=0⇒x2−37x−8x+296=0, Here we use splitting the middle term method ⇒x(x−37)−8(x−37)=0⇒(x−8)(x−37)=0So⇒x=8 and 37 At x =8 we get the dimension of the pond, As: Length of pond =50−2x=50−2×8=50−16=34 m And Breadth of pond =40−2x=40−2×8=40−16=24 m And at x = 37 we get dimension of pond , As: Length of pond =50−2x=50−2×37=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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