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 + bÂ= 40Or,Â

bÂ = 40 â€“ÂlArea of the rectangular park =Â

lÃ—b = l(40 â€“ l) =Â40lÂâ€“Âl^{2 }= 400l^{2}Ââ€“^{Â Â }40lÂ + 400Â= 0, which is a quadratic equation.Comparing the equation withÂ

ax^{2}Â +ÂbxÂ+ÂcÂ = 0, we getaÂ = 1,ÂbÂ = -40,ÂcÂ = 400Since, Discriminant =Â

b^{2}Â â€“ 4ac=(-40)^{2}Â â€“ 4 Ã— 400= 1600 â€“ 1600 = 0

Thus,

b^{2}Â â€“ 4acÂ= 0Therefore, this equation has equal real roots. Hence, the situation is possible.

Root of the equation,

lÂ = â€“b/2alÂ = (40)/2(1) = 40/2 = 20Therefore, length of rectangular park,Â

lÂ= 20 mAnd breadth of the park,Â

bÂ= 40 â€“ÂlÂ= 40 â€“ 20 = 20 m.