Question -
Answer -
Let the length and breadth of the parkbe 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 thepark, b = 40 – l = 40 – 20 = 20 m.