Minimum cost of an area of fencing using derivatives

[Physics345]

Homework Statement

A homeowner wishes to enclose a rectangular garden with fencing. The garden will be adjacent to his neighbour’s lot. There will be fencing on all four sides. His neighbour will be paying for half the shared fence.

a) What should the dimensions of the garden be if the area is 432 m^2 and the homeowner would like to keep his share of the cost to a minimum? Include a diagram.

b) At $45/m, what is the homeowner’s cost? What is the neighbor's cost?

Homework Equations

The Attempt at a Solution

For this question my main issue is the wording in the question I'm not sure exactly what it wants. Does it want me to find the homeowner/neighbors individual dimensions, or the dimensions of the whole garden.
Anyways here's what I've done so far let me know what you guys think.
Also on a side note, I wrote a whole bunch of stuff out on word, to ask about, so I'm just posting all of them at once on different threads (In case anyone was wondering about the multiple threads I just posted)

 

[DrClaude]

As I said in your other thread, your answer is hard to follow. It would help a lot if you typed your answer directly, see https://www.physicsforums.com/help/latexhelp/

For this question my main issue is the wording in the question I'm not sure exactly what it wants. Does it want me to find the homeowner/neighbors individual dimensions, or the dimensions of the whole garden.

I think that the problem is quite clear: "What should the dimensions of the garden be?" The answer should be the dimensions of the sides of the rectangle, with a specification as to which side is adjacent with the neighbour.

Your answer is correct.

 

[Physics345]

I need to stop doubting my self when I'm relatively sure the answer is correct. The doubt will go away with more practice hopefully.
Once again thank you!

 

[Mark44]

Thread moved. @Physics345, please post questions that involve derivatives in the Calculus & Beyond section, not in the Precalc section.