Question 941039
{{{A=(1/2)wh=63}}}
{{{h=2w-3}}}
Substituting,
{{{(1/2)w(2w-3)=63}}}
{{{2w^2-3w=126}}}
{{{2(w^2-(3/2)w)=126}}}
{{{w^2-(3/2)w+9/16=63+9/16}}}
{{{(w-3/4)^2=1017/16}}}
{{{w-3/4=0 +- sqrt(1017)/4}}}
Only the positive solution makes sense here.
{{{w=3/4 + (3/4)sqrt(113)}}}
{{{w=(3/4)(1 + sqrt(113))}}}
{{{h=2(3/4)(1 + sqrt(113))-3}}}
{{{h=(3/2)(1 + sqrt(113))-3}}}
{{{h=-3/2 + (3/2)sqrt(113)}}}
{{{h=(3/2)(sqrt(113)-1)}}}