What are the smallest dimensions of a property that will satisfy a pool being 400 sq. ft. with a 2 ft. deck on each side as well as a 7 ft ft. deck in front and back?

Okay, loaded question. I suggest that you get out your deed which will tell you the measurements of your property lines and even then, it's a stretch because the pool has to be within a certain amount of feet of property line (I think), see where you house sits as opposed to your back yard or wherever you want the pool (inground or above ground it makes a big difference) and call your township office, then consult the municipality. Cause, my friend, we don't know where you are and it all matters. So give us more information.

We can use a little calc to solve this.

Let x = the pool width and y=the pool length.

The area of the pool is xy=400... [1]

The area of the entire region including the walk is:

A=(x+4)(y+14)... [2]

Solve [1] for y and sub into [2]:

(x+4)(\frac{400}{x}+14)=14x+\frac{1600}{x}+456

Differentiate:

\frac{dA}{dx}=14-\frac{1600}{x^{2}}

Now, set to 0 and solve for x. Only one solution will be good because the other will be negative.

Then find y and your done.