In a rectangular park of dimensions 50 m x 40 m, a rectangular pondis constructed so that the area of grass strip of uniform widthsurrounding the pond would be 1184 m^2. Find the length and breadthof the pond.

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

1.	In a rectangular park of dimensions 50 m x 40 m, a rectangular pondis constructed so that the area of grass strip of uniform widthsurrounding the pond would be 1184 m^2. Find the length and breadthof the pond.
Answer» Dimensions = 50 m and 40 mArea of the rectangular lawn= 50× 40 = 2000 m²Area of the grass surrounding the pond = 1184 m²So, the area of the pond = area of the lawn - area of the grass= 2000 - 1184Area of the pond = 816 m²Let the width of around the pond be 'x' mThen, the length of the pond = (50 - 2x) mand the breadth of the pond = (40 - 2x) mArea of the pond = 816 m²⇒ (50 - 2x) ×(40-2x) = 8162000 - 80x - 100x + 4x² = 8164x² - 180x + 2000 - 816 = 04x² - 180x + 1184 = 0dividing it by 4 we getx² -45x + 296 = 0x² - 37x - 8x + 296 =0x(x-37) - 8(x-37) = 0(x-37) (x-8) = 0x= 37 or x = 8supposeif x = 37, thenthe length of the pond will be 50 - 23750 - 74 = -24m, which is not possible because length cannot be negative.Therefore the length of the pond = 50 - 2850 - 16 = 34 mandBreadth of the pond = 40 - 2*840 - 16 = 24 mLength = 34 m and breadth = 24 m