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Question 5
Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth.

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Solution

Let the length and breadth of the park be l and b.
Perimeter = 2 (l + b) = 80
l + b= 40
Or,b= 40 -l
Area=l×b=l(40l)=40ll2=400
l240l+400=0
Comparing this equation with ax2+bx+c=0, we get
a = 1, b = -40, c = 400
Discriminant=b24ac
= (40)24×400
= 1600 - 1600
= 0
Therefore, this equation has equal real roots. And hence, this situation is possible.
Root of this equation =b2a = 402×1 = 402 = 20
Therefore, length of the park,l= 20 m

and breadth of the park, b= 40 -l= 40 - 20 = 20 m.

So the park will be of square shape with a side length of 20m.

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