Question 947609
h, height of poster
w, width of poster
u, uniform width or margin around the printing
A, area of printing on the poster
GIVEN:
h=2w
u=2
A=70


You should draw a picture of this  (not shown in this solution).


Total poster area:  {{{h*w}}}.
Printed or typed area:  {{{(h-2u)(w-2u)=A}}}, note how the dimensions of the printed area are less than the poster area.
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Notice that the unknown variables in that equation are h and w.


Simplify the Printed Area equation:
{{{hw-2uw-2uh+4u^2-A=0}}}
Substitute for h=2w.
{{{2w^2-2uw-2u*2w+4u^2-A=0}}}
{{{2w^2-2uw-4uw+4u^2-A=0}}}
{{{highlight_green(2w^2-6uw+4u^2-A=0)}}}------you can continue this way symbolically and solve this quadratic equation for w, but you can also take advantage of your known even number value for A=70 NOW...


{{{2w^2-6uw+4u^2-70=0}}}
{{{w^2-3uw+2u^2-35=0}}}
and you also know u=2, so ...
{{{w^2-6w+8-35=0}}}
{{{highlight_green(w^2-6w-27=0)}}}-----Most convenient is to solve this equation for w.   ....  Factorable?


{{{(w-9)(w+3)=0}}}
The meaningful value is {{{highlight(w=9)}}}.
AND
{{{highlight(h=2w=18)}}}.