Is it possible to design a rectangular park of perimeter 80m. and area 400m2? If so, find its length and breadth.
Let Length of rectangular park be x and breadth be (40 - x)
Area = 400 m2
⇒ x(40 - x) = 400
⇒ x2 - 40x + 400 = 0
Discriminant = ( - 40)2 - 4 × 1 × 400
⇒ Discriminant = 1600 - 1600 = 0
Since Discriminant is 0 so it is possible
x2 - 40x + 400 = 0
⇒ (x - 20)2 = 0
⇒ x = 20 m
Answer: Length = 20m, Breadth = 20m