# The function that models perimeter of a rectangle in terms of its length x whose area is 16 m 2 . ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2, Problem 6P
To determine

## To find: The function that models perimeter of a rectangle in terms of its length x whose area is 16 m2 .

Expert Solution

The function that models area of given rectangle is 2(x2+16x) .

### Explanation of Solution

Perimeter of a rectangle is,

P=2(x+w)

Eliminate w from equation (1) and model the function into single variable x .

Area of rectangle is,

A=(xw)

Substitute 16 for A in above equation and solve for w .

16=xww=16x

Summarize all the information in a table as shown below.

 In Words In Algebra Length x Width 16x

Use the information in the table and model the function.

P=2(x+w)=2(x+16x)=2(x2+16x)

Thus, the function that models area of given rectangle is 2(x2+16x) .

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