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5. Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, findits length and breadth. |
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Answer» Let the length and breadth of the park be l and b.Perimeter = 2 (l + b) = 80l + b= 40Or,b= 40 -lArea =l×b = l(40 - l) =40l-l240l- l2= 400l2-40l+ 400= 0Comparing this equation withal2+bl+c= 0, we geta= 1,b= -40,c= 400Discriminant =b2- 4ac(-40)2- 4 × 400= 1600 - 1600 = 0b2- 4ac= 0Therefore, this equation has equal real roots. And hence, this situation is possible.Root of this equation,l= -b/2al= (40)/2(1) = 40/2 = 20Therefore, length of park,l= 20 mAnd breadth of park,b= 40 -l= 40 - 20 = 20 m. |
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