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

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

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) = 40l – l² = 400

l² –  40l + 400 = 0, which is a quadratic equation.

Comparing the equation with ax² + bx + c = 0, we get

a = 1, b = -40, c = 400

Since, Discriminant = b² – 4ac

=(-40)² – 4 × 400

= 1600 – 1600 = 0

Thus, b² – 4ac = 0

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

The root of the equation,

l = –$\frac{b}{2a}$

l = $\frac{-(-40)}{2\left(1\right)}$ = 20

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

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