finding the plot of land with least area.?

Question

area of the pool without sidewalk is 1000ft^2. let x be the length of one side of the pool .
the pool is required to have a walk of uniform width 2 ft surrounding it.

how do you find the dimensions of the plot of land (pool plus sidewalk).that has the least area. what is the least area?

i believe that the equation will be 4x+(4000/x)+1016

i am asking for the least area, not max

Answer 1

If x is one side of the pool, the other side will be 1000/x

The pool + sidewalk will be (x+2) by (1000/x) + 2

Area = (x+2)(2+1000/x)
= (x+2)(2x + 1000)/x
= (2x^2 + 4x + 1000x + 2000)/x
= 2x + 1004 + 2000/x

Max area will come when A' = 0
A' = 2 - 2000/x^2
so 0 = 2- 2000/x^2
2 = 2000/x^2
2x^2 = 2000
x^2 = 1000
x = 10 sqrt(10)
The other side is 1000/(10 sqrt(10)= 100/sqrt(10) = 10 sqrt(10)

So the plot of land will be 2+10sqrt(10) feet square

Answer 2

If adding a walkway around the pool, the smallest walkway will add the smallest additional area. (The area of the pool is already fixed.)
That would require a pool that was round in shape. (A side "X" implies a straight side. Is additional data needed to help with this question?)
You do the math.