Rectangle optimization - possible text error

[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.

 

[Ray Vickson]

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.View attachment 207796

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

 

[SammyS]

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

 

[quicksilver123]

Anyone confirm that the answer I got is correct?

 

[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.

 

[scottdave]

Anyone confirm that the answer I got is correct?

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

 

[haruspex]

there was a typo in the middle (x should have been 2x)

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) =