How i solve the question of quadratic equation of exercise 4.4 of class 10th math. The best way for solving this question is 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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# Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth. Q.5

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Let the length and breadth of the park be

land b.Perimeter of the rectangular park = 2 (

l + b) = 80So, l + b= 40Or,

b= 40 –lArea of the rectangular park =

l×b = l(40 – l) =40l–l^{2 }= 400l^{2}^{ }40l+ 400Comparing the equation with

ax^{2}+bx+c= 0, we geta= 1,b= -40,c= 400Since, Discriminant =

b^{2}– 4ac=(-40)^{2}– 4 × 400= 1600 – 1600 = 0

Thus,

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

Root of the equation,

l= –b/2al= (40)/2(1) = 40/2 = 20Therefore, length of rectangular park,

l= 20 mAnd breadth of the park,

b= 40 –l= 40 – 20 = 20 m.