5. Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth.

Let the length and breadth of the park be l and b. Perimeter of the rectangular park = 2 (l + b) = 80 So, l + b = 40 Or, b = 40 – l Area of the rectangular park = l×b = l(40 – l) = 40l – l2 = 400 l2 – 40l + 400 = 0, which is a quadratic equation. Comparing the equation with ax2 + bx + c = 0, we get a = 1, b = -40, c = 400 Since, Discriminant = b2 – 4ac =(-40)2 – 4 × 400 = 1600 – 1600 = 0 Thus, b2 – 4ac = 0 Therefore, this equation has equal real roots. Hence, the situation is possible. Root of the equation, l = –b/2a l = (40)/2(1) = 40/2 = 20 Therefore, length of rectangular park, l = 20 m And breadth of the park, b = 40 – l = 40 – 20 = 20 m.