**Solution:**

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

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) = *40*l *– *l*^{2 }= 400

*l*^{2} – 40*l* + 400 = 0, which is a quadratic equation.

Comparing the equation with *ax*^{2} + *bx *+ *c* = 0, we get

*a* = 1, *b* = -40, *c* = 400

Since, Discriminant = *b*^{2} – 4*ac*

*=(-*40*)*^{2} – 4 × 400

= 1600 – 1600 = 0

Thus,* b*^{2} – 4*ac *= 0

Therefore, this equation has equal real roots. Hence, the situation is possible.

The root of the equation,

*l* = –*b*/2*a*

*l* = -(-40)/2(1) = 40/2 = 20

Therefore, the length of the rectangular park, *l *= 20 m

And the breadth of the park, *b *= 40 – *l *= 40 – 20 = 20 m.