# Homework Help: Rectangle optimization - possible text error

1. Jul 25, 2017

### quicksilver123

Hi,
I may have discovered a textbook error but I'm no calc whiz. I need an assist to find out if the question unintentionally described a square instead of a rectangle.
I have attached the textbooks solution as well as my attempt at a solution.
The numbers check out, I just want to make sure before I submit a request for review to the author (my prof). Of course there's always the potential that he's just trying to be a tricky guy.

2. Jul 25, 2017

### Ray Vickson

The book's equation
$$P(x) = x + \frac{440}{x}$$
should be
$$P(x) = 2x + \frac{440}{x}$$

3. Jul 25, 2017

### SammyS

Staff Emeritus
A square IS a rectangle; a rectangle with all sides of equal length.

4. Jul 25, 2017

### quicksilver123

Anyone confirm that the answer I got is correct?

5. Jul 25, 2017

### scottdave

Yes there was a typo in the middle (x should have been 2x), but they apparently carried it through to get the correct answer. One thing to notice about this problem @quicksilver123 is that if you have a rectangle, and you want to maximize area for a given perimeter, the result will be a square. Or if you want to minimize perimeter for a given area, it essentially the same problem, and the result is a square.

6. Jul 25, 2017

### scottdave

Yes Length = Width = sqrt(220) cm. Always remember the units.

7. Jul 25, 2017

### haruspex

I don't think it was a typo. There is a band of erasure running near-vertically through several lines of text. It wipes out the portions in bold below:

for area is A=xy
We know that xy
P(x) = 2 x
P''(x) =