Expert: Paul Klarreich - 2/23/2011

Question
College Precalculus; Modeling with functions


A rectangle has an area of 22 m^2. Find a function that models its perimeter P in terms of the length of one of its sides x.

I know that the area of a rectangle is width times height, A=lh. The perimeter of a rectangle is P=2l+2h. I have read through the section, and it only demonstrates an example of finding the maximum area based upon the perimeter given. I do not know where to start to work backwards based on this.

Answer
Questioner: Christina
Country: United States
Category: Advanced Math
Private: No
Subject: Function that models perimeter
Question: College Precalculus; Modeling with functions


A rectangle has an area of 22 m^2. Find a function that models its perimeter P in terms of the length of one of its sides x.

I know that the area of a rectangle is width times height, A=lh. The perimeter of a rectangle is P=2l+2h. I have read through the section, and it only demonstrates an example of finding the maximum area based upon the perimeter given. I do not know where to start to work backwards based on this.
..................................
A famous mathematician (no, not me) said:

Rewording a problem is the equivalent of solving it.

Let's try:

Find a function that models its perimeter P in terms of the length of one of its sides x.

is the same as:

Express the perimeter P of a rectangle whose area is 22 in terms of one of its sides x.
...........................
"I know that the area of a rectangle is width times height, A=LH"

becomes

I know that A = LH, where one of the sides is x.
.......................
I wonder, then, if we call x the width, what the length would be.


That means  A = Lx, and so L would be expressed as:

.................................

Darn!! I just ran out of ink.  You will have to finish up.