I just hope I'm not too late
for the wire question
4x+2pir=80
r=80-4x/2pi
Area=x2+pi. r2
substitute 80-4x/2pi for r
x2+(pi X (80-4x)/2pi)2
when u open it u get
x2+ (p X 6400-640+16x2)/ 4pi2
to make denominator same
(4pi x2+ p X 6400-640+16x2)/ 4pi2
reduce...that is divide by 4 and group common terms
(pi+4)2+1600-160/ pi
for the second part
dA/dx= 2x(pi+4)x-160/ pi= 0
solve to get value of x
I will try the vector sum...but I haven't done it in class...so it will take some time