Question 731276
What are A, B, and C supposed to be?


Just use what you know about a rectangle and the given information about the problem.  


Let's say w = width of the rectangle and h = height of the rectangle.
Perimeter is 2w+2h=36.
Area is wh=65.


Pick one of the equations, any one of them.  Solve for one of the variables, w or h; it does not matter which.  Substitute that formula into the other equation.  Now you should have what will be a quadratic equation.  You may need to simplify it before using it.  


A possible way to go,
{{{2h+2w=36}}}
{{{2h=36-2w}}}
{{{h=18-w.}}}
-------------
{{{wh=65}}}, to continue starting with area relationship
{{{w(18-w)=65}}}, substituting what was found for h
{{{18w-w^2=65}}}
{{{-w^2+1w8=65}}}
{{{-w^2+18w-65=0}}}
{{{highlight(w^2-18w+65=0)}}}
You can certainly use the general solution to quadratic formula if you want to but that polynomial seems factorable.  I will use quadratic formula solution.


{{{w = (18+sqrt(18^2-4*65))/2}}}
{{{w=(18+sqrt(64))/2}}}
{{{w=(18+8)/2}}}
{{{highlight(w=13)}}}
OR
{{{w=(18-sqrt(18^2-4*65))/2}}}
{{{w=(18-8)/2}}}
{{{highlight(w=5)}}}


That was for w.  You can then use either the perimeter equation or the area equation to find h.


postnote:  You probably meant Ax^2+Bx+C=0 when you mentioned some confusion about "A, B, and C".