# The function that models area of a rectangle in terms of its length x whose perimeter is 20 ft . ### 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 5P
To determine

## To find: The function that models area of a rectangle in terms of its length x whose perimeter is 20 ft .

Expert Solution

The function that models area of given rectangle is 10xx2 .

### Explanation of Solution

The formula to calculate area of rectangle is,

Area=length×width

Length of the rectangle is x .

Perimeter of rectangle is,

P=2(x+w)

Substitute 20 for P in above equation and solve for w .

20=2(x+w)10=(x+w)10x=(x+w)x10x=w

Add x to both the sides of above equation.

10x=(x+w)x10x=w

Summarize all the information in a table as shown below,

 In Words In Algebra Length x Width 10−x

Use the information in the table and model the function.

Area=length×widthA=x(10x)=10xx2

Thus, the function that models area of given rectangle is 10xx2 .

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