Exercise 4.4 problem 5 .10th NCERT …

5. Is it possible to design a rectangular park of perimeter 80 metres and area 400 m2. If so, find its length and breadth. Ans. Let length of park = x metres We are given area of rectangular park =  Therefore, breadth of park =  metres{Area of rectangle = length × breadth} Perimeter of rectangular park = 2 (length + breath) = metres We are given perimeter of rectangle = 80 metres According to condition: =>  ⇒  ⇒  ⇒  ⇒  Comparing equation,  with general quadratic equation , we get a = 1, b = −40 and c = 400 Discriminant =  (1) (400) = 1600 – 1600 = 0 Discriminant 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 . Using quadratic formula  to solve equation,  Here, both the roots are equal to 20. Therefore, length of rectangular park = 20 metres Breadth of rectangular park =