Question -
Answer -
Let the length and breadth of the parkbe┬аl┬аand b.
Perimeter of the rectangular park = 2 (l +b) = 80
So, l + b┬а= 40
Or,┬аb┬а= 40 тАУ┬аl
Area of the rectangular park =┬аl├Чb =l(40 тАУ l) =┬а40l┬атАУ┬аl2┬а= 400
l2┬атАУ┬а┬а40l┬а+400┬а= 0, which is a quadratic equation.
Comparing the equation with┬аax2┬а+┬аbx┬а+┬аc┬а=0, we get
a┬а= 1,┬аb┬а=-40,┬аc┬а= 400
Since, Discriminant =┬аb2┬атАУ4ac
=(-40)2┬атАУ4 ├Ч 400
= 1600 тАУ 1600 = 0
Thus,┬аb2┬атАУ 4ac┬а=0
Therefore, this equation has equal real roots.Hence, the situation is possible.
Root of the equation,
l┬а= тАУb/2a
l┬а= (40)/2(1) =40/2 = 20
Therefore, length of rectangular park,┬аl┬а=20 m
And breadth of thepark,┬аb┬а= 40 тАУ┬аl┬а= 40 тАУ 20 = 20 m.