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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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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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1. Let the length and breadth of the park be l and b.

Perimeter of the rectangular park = 2 (l + b) = 80

So, l + bÂ = 40

Or,Â bÂ = 40 â€“Â l

Area of the rectangular park =Â lÃ—b = l(40 â€“ l) =Â 40lÂ â€“Â l2 = 400

l2Â â€“Â Â 40lÂ + 400Â = 0, which is a quadratic equation.

Comparing the equation withÂ ax2Â +Â bxÂ +Â cÂ = 0, we get

aÂ = 1,Â bÂ = -40,Â cÂ = 400

Since, Discriminant =Â b2Â â€“ 4ac

=(-40)2Â â€“ 4 Ã— 400

= 1600 â€“ 1600 = 0

Thus, b2Â â€“ 4acÂ = 0

Therefore, this equation has equal real roots. Hence, the situation is possible.

Root of the equation,

lÂ = â€“b/2a

lÂ = (40)/2(1) = 40/2 = 20

Therefore, length of rectangular park,Â lÂ = 20 m

And breadth of the park,Â bÂ = 40 â€“Â lÂ = 40 â€“ 20 = 20 m.

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