I've checked it and I get the same result.
triangle wire length = y
square wire length = x
Ssquare = (x/4)^2
Striangle = (sqrt(3)/36)*y^2
Stotal = (x/4)^2 + (sqrt(3)/36)*y^2
subject to x+y = 10
I've plugged in x = 10-y ,and took the derivative of Stotal with respect to y...