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

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

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
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

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