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

Dear Student


Let the length and breadth of the park beland b.
Perimeter of the rectangular park = 2 (l + b) = 80
So,
l + b= 40
b= 40 -l

Area of the rectangular park =l×b
400= l(40 - l)
400=40l-l^2
0 = l^2- 40l+400 ,
which is a quadratic equation.

Comparing the equation withax^2+bx+c= 0,
a= 1,b= -40,c= 400

Since, Discriminant =b^2- 4ac
D=(-40)^2- 4 × 400
=> 1600 - 1600 = 0

Thus,b^2-4ac=0
Therefore, this equation has equal real roots.
Hence, the situation is possible.

Root of the equation,
l=20.

Therefore, length of rectangular park,l= 20 m
breadth of the park,b= 40 -l= 40 - 20 = 20 m.

Thanks