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


Let the length and breadth of the park be l and b.

Perimeter = 2 (l + b) = 80


l + b = 40 Or, b = 40 – l


Area = l × b = l (40 − l)


= 40ll2= 400 Given


l2 − 40l + 400 = 0


Comparing this equation with al2 + bl + c = 0, we obtain


a = 1, b = −40, c = 400


Discriminant = b2 − 4ac = (− 40)2 −4 (1) (400) = 1600 − 1600 = 0


As b2 − 4ac = 0,


Therefore, this equation has equal real roots.


And hence, this situation is possible.


Root of this equation,




Therefore, length of park, l = 20 m


And breadth of park, b = 40 − l = 40 − 20 = 20 m


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