5. Is it possible to design a rectangular park of perimeter 80 metres and area 400\xa0m2. If so, find its length and breadth.Ans.\xa0Let length of park =\xa0x\xa0metresWe are given area of rectangular park =\xa0Therefore, breadth of park =\xa0\xa0metres{Area of rectangle = length ×\xa0breadth}Perimeter of rectangular park = 2 (length\xa0+\xa0breath) =\xa0metresWe are given perimeter of rectangle = 80 metresAccording to condition:=>\xa0⇒\xa0⇒\xa0⇒\xa0⇒\xa0Comparing equation,\xa0\xa0with general quadratic equation\xa0, we get\xa0a\xa0= 1,\xa0b\xa0= −40 and\xa0c\xa0= 400Discriminant =\xa0\xa0(1) (400) = 1600 – 1600 = 0Discriminant is equal to 0.Therefore, two roots of equation are real and equal which means that it is possible to design a rectangular park of perimeter 80 metres and area\xa0.Using quadratic formula\xa0\xa0to solve equation,Here, both the roots are equal to 20.Therefore, length of rectangular park = 20 metresBreadth of rectangular park =\xa0