In a rectangular park of dimensions 50 m x 40 m, a rectangular pondthe area of grass strip of uniform widthsurrounding the pond would be 1184 m sq. Find the length and breadth of the pond.

In a rectangular park of dimensions 50 m x 40 m, a rectangular pondthe

1.	In a rectangular park of dimensions 50 m x 40 m, a rectangular pondthe area of grass strip of uniform widthsurrounding the pond would be 1184 m sq. Find the length and breadth of the pond.
Answer» Given, dimensions of rectangular park = 50mx40mSo, Are of park = 50*40 = 2000sq.mArea of the grass strip surrounding the pond = 1184 sq.mHence, area of the pond = lb = 2000-1184 = 816sq.m ⇒ lb = 816sq.mLet 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=8But x=37 is not possible∴ Width of the grass strip = 8mLength of the pond = 50-16 = 34mBreadth of the pond = 40-16 = 24m