Question 825779
x = base
y = altitude

{{{xy(1/2)=165}}}
If {{{y=x+7}, then {{{x(x+7)(1/2)=165}}};
{{{x^2+7x=165*2}}}
{{{x^2+7x-330=0}}} ------ Is this factorable?


330=3*2*5*11


Look at discriminant:  {{{7*7-4*(-330)=49+1320}}};
{{{sqrt(1320)=sqrt(4*330)=2*sqrt(330)}}}.  The quadratic member is not factorable.


base:{{{highlight(x=(-7+2*sqrt(330))/2)}}} OR {{{highlight(x=-7/2+sqrt(330))}}};
'
altitude: {{{y=(-7+2*sqrt(330))/2)+7}}}
{{{-7/2+sqrt(330)+14/2}}}
{{{highlight(7/2+sqrt(330))}}}