Question 1055386
Given the similarity between the two rectangles, that is already the justification for {{{a/y=y/(a-1)}}}.  The reason is, their similarity is given.  The equation, replacing your "1" with a "y" is simply the proportion for comparing the corresponding rectangular parts.



{{{a(a-1)=y^2}}}
{{{a^2-a-y^2=0}}}
skipping trying to complete square;
{{{a=(1+- sqrt(1+4y^2))/2}}}, and probably want the PLUS form.