Calculus, 8th Edition,stewart; page 22 problem 58

Question

Find a formula for the described function and state its domain.

A rectangle has area 16 m^2. Express the perimeter of the rectangle as a function of the length of one of its sides.

Answer 1

Step:1

The area of the rectangle  m.

But area of a rectangle is .

Where  is the length of the rectangle.

           is the breadth of the rectangle.

Find  in terms of .

.

Step:2

Perimeter of a rectangle is .

Find the expression for perimeter of the rectangle in terms of .

Substitute  in the above expression.

Domain :

The denominator of the function  should not be a zero.

So .

But perimeter can not be a negative.

All positive real numbers of  is the domain of the function .

The domain of the  is .

Solution:

.

The domain of the  is .