Question 980091
area, {{{39=(1/2)a*b}}};
a for altitude
b for base length;


The description of the "one side" makes it the base.
{{{b=2a+1}}}.


{{{(1/2)a*b=39}}}
{{{(1/2)a(2a+1)=39}}}
{{{a^2+a=78}}}
{{{a^2+a-78=0}}}


{{{78=2*3*13=6*13}}}, so factoring the polynomial will not work.


Discriminant:  {{{1^2-4(-78)=1+4*78=313}}}.  PRIME NUMBER.


{{{a=(-1+sqrt(313))/2}}} and the PLUS form is needed.


b=2a+1
{{{b=2((-1+sqrt(313))/2)+1}}}