# The function of the perimeter of the rectangle in terms of the length of one of the sides of rectangle and the function domain.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1.1, Problem 54E
To determine

## To find: The function of the perimeter of the rectangle in terms of the length of one of the sides of rectangle and the function domain.

Expert Solution

The formula for the function of perimeter of the rectangle in terms of its length is P(l)=2l2+32l .

The domain of the function of the perimeter (P) of the rectangle in terms of its length is l>0 .

In case of length is to be larger than breadth, the domain of P is l>4 .

### Explanation of Solution

Given:

The area of the rectangle is 16m2 .

Formula used:

Area of the rectangle, A=l×b , where ‘l’ is the length of the rectangle and ‘b’ is the breadth of the rectangle.

Perimeter of the rectangle, P=2(l+b) , where ‘l’ is the length of the rectangle and ‘b’ is the breadth of the rectangle.

Calculation:

Let the length of the rectangle be l and the breadth be b. Since the area of the rectangle is 16m2 ,

l×b=16m2 (1)

Express the equation (1) in terms of length.

l×b=16b=16l

Therefore, the function of perimeter of the rectangle in terms of l is P(l)=2(l+16l) .

That is, P(l)=2l+32l .

Therefore, the function of perimeter of the rectangle in terms of its length is P(l)=2l2+32l .

The domain of P is l>0 as the length l cannot take the negative values.

In the case of length is to be larger than breadth, the domain of P is l>4 .

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