A 51 meter length of wire is cut into two parts. The first part is fashioned into a rectangle that is twice as long as it is wide. The second part is fashioned into a square. How much of the originial wire is used for each shape if the shapes' combined area is a minimum? Use the second derivative test(S.D.T.) to determine the minimum.
[tex]A = xy + x^2[/tex]
[tex]51 = 2(2x + y) + 4x[/tex]