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

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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.

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.