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)

= 40l − l²= 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