Question

A wire is 72 cm long.It is bent to form a rectangle. Fimd its dimensions when its area is maximum

Answer 1

Answer:

18 cm by 18 cm

Step-by-step explanation:

Let x and y be the lengths of the sides of the rectangle.

Perimeter = 2x + 2y = 72  => x + y = 36 => y = 36 - x

Area = A = xy = x ( 36 - x )

Plotting A = x ( 36 - x ), this is a parabola with x-intercepts at x=0 and x=36.

It reaches its maximum at the vertex in between these, so at x = (0+36)/2 = 18.

[ Alternatively, A = -x² + 36x, so the vertex is at x = -b/2a = -36/(-2) = 18. ]

The other side is then y = 36 - x = 36 - 18 = 18.

So the area is a maximum when it is a square with side 18cm.

Answer 2

Answer:

Step-by-step explanation:

Use 2( l+b)=72m

And hence you will get l+b=36

L=36-b and b=36-l

Now multiply them