India - Location, Latitudinal and Longitudinal Extent
In a rectangu...
Question
In a rectangular park of dimensions 50m×40m, a rectangular pond is constructed so that the area of grass strip of uniform width surrounding the pond would be 1184m2.Find the length and breadth of the pond.
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Solution
Given, dimensions of rectangular park = 50mx40m So, Are of park = 50*40 = 2000m² Area of the grass strip surrounding the pond = 1184 m² Hence, area of the pond = lb = 2000-1184 = 816m² Take lengthlength=l and breadth= b
⇒ lb = 816m²
Let the width of the grass strip be 'x' So, (50-2x)(40-2x) = 816 ⇒ 2000 - 100x - 80x + 4x² = 816 ⇒ 2000-180x+4x² = 816 ⇒4x²-180x+1184 = 0 ⇒x²-45x+296 = 0 ⇒x²-37x-8x+296=0 ⇒x=37, x=8 But x=37 is not possible ∴ Width of the grass strip = 8m Length of the pond = 50-16 = 34m Breadth of the pond = 40-16 = 24m