Question

in years was 48.
5. Is it possible to design a rectangular park of perimeter 80 m 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 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.

Root of the equation,

l = –b/2a

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

Therefore, length of rectangular park, l = 20 m

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