Question

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

Answer 1

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

40l − l² = 400

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