Question

A wire of length 20cm is to bent to form a rectangle find the maximum and minimum area

Answer 1

maximum 25
minimum 9
hope it will help you

Answer 2

Answer:

The maximum area of rectangle is 25 cm² and the minimum area of rectangle can not be determined.

Step-by-step explanation:

It is given that A wire of length 20 cm is to bent to form a rectangle. It means the perimeter of the rectangle is 20 cm.

The perimeter of a rectangle is

$P=2(l+w)$

$20=2(l+w)$

$10=l+w$

Let the length of rectangle be x and width of the rectangle is (10-x).

The area of rectangle is

$A=l\times w$

$A=x(10-x)$

$A=10x-x^2$

Differentiate with respect to x.

$\frac{dA}{dx}=10-2x=0$

$x=5$

Differentiate with respect to x.

$\frac{d^2A}{dx^2}=-2<0$

Since $\frac{d^2A}{dx^2}<0$, therefore only maximum value of function exist.

The area of rectangle is maximum at x=5. If x=5, then the area of rectangle is

$A=5(10-5)=25$

Therefore the maximum area of rectangle is 25 cm² and the minimum area of rectangle can not be determined.