Question

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

Answer 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