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).
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embizze | High School Teacher | (Level 1) Educator Emeritus

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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:

20=2l+2w 

==> 2w=20-2l

==> w=10-l

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

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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.

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