A rectangle has a perimeter of 20m.  Express the area of the rectangle as a function of the length of ones of its sides.

Textbook Question

Chapter 1, 1.1 - Problem 57 - Calculus: Early Transcendentals (7th Edition, James Stewart).
See all solutions for this textbook.

1 Answer | Add Yours

embizze's profile pic

embizze | High School Teacher | (Level 2) Educator Emeritus

Posted on

The perimeter of a rectangle can be written as P=2l+2w where w is the width and l the length.

Here P=2l+2w or 20=2l+2w

The area of a rectangle is A=lw.

We can express the width of the rectangle in terms of its length:


==> 2w=20-2l

==> w=10-l

Thus the area is A=(10-l)l


The area of a rectangle with perimeter 20 can be written as:

`A=10l-l^2` where l is the length of one of the sides of the rectangle.


We’ve answered 319,647 questions. We can answer yours, too.

Ask a question