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...