A metal wire 36cm long is bent to form a rectangle find its dimensions when its area is maximum​

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1. Answer:

   Let the length and breadth of a rectangle be I and b.

   .. Perimeter of rectangle = 2 (1 + b) =

   36cm

   .:. 1+b=18

   Area of rectangle = 1x b = 1 (18-1)

   Let f(1) = 181-12

   f(1) = 18-21

   and f(1) = -2

   Consider, f ‘(I) = 0

   .. 18-21 0

   .. 18 = 21

   l= 9

   For 1 = 9,

   f”(9) = -2 <0

   .. f(x), i.e. area is maximum when I

   cm

   and b = 18-9 [form (i)]

   = 9 cm

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