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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.

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one month ago Anand Kumar Pandey
1452 Points
```							Dear StudentLet the length and breadth of the park beland b.Perimeter of the rectangular park = 2 (l + b) = 80So,l + b= 40b= 40 -lArea of the rectangular park =l×b400= l(40 - l)400=40l-l^20 = l^2- 40l+400 ,which is a quadratic equation.Comparing the equation withax^2+bx+c= 0,  a= 1,b= -40,c= 400Since, Discriminant =b^2- 4acD=(-40)^2- 4 × 400=> 1600 - 1600 = 0Thus,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 mbreadth of the park,b= 40 -l= 40 - 20 = 20 m.Thanks
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one month ago
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