Question 887291
Two starting lengths from the wire, {{{u+v=30}}}.


The square:  x for one side length.  Area is {{{x^2}}}.


The rectangle:  2y to y may be the sides ratio.   Area is {{{2y^2}}}. 


If assign S as the sum of the areas, then {{{highlight_green(S=x^2+2y^2)}}}.


Accounting for the sum of perimeters to be 30 is also needed.
Back with u and v, 
{{{u=4x}}} and {{{v=2(2y)+2y}}}----based on the given ratio of its dimensions.
{{{u=4x}}} and {{{v=6y}}}.
{{{4x+6y=30}}}
{{{highlight_green(2x+3y=15)}}}---THIS equation can be used to substitute for either x or y in the S equation.  You can then determine the minimum value for S.


Maybe you can take the pathway to the solution described.