Question

in the centre of a rectangulae lawn of dimension 50 × 40 cm a rectangular pond is to be constructed so that the area of grass surrounding the pond would be 1184 cm sq find the dimension of the pond

Answer 1

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' m Then, 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 = 0 dividing it by 4 we getx² - 45x + 296 = 0 x² - 37x - 8x + 296 =0x(x - 37) - 8(x - 37) = 0(x - 37) (x - 8) = 0x = 37 or x = 8suppose if x = 37, thenthe length of the pond will be 50 - 2*37 50 - 74 = - 24m, which is not possible because length cannot be negative.Therefore the length of the pond = 50 - 2*850 - 16 = 34 mand Breadth of the pond = 40 - 2*840 - 16 = 24 mLength = 34 m and breadth = 24