Question 82612
20X12 cm are the outside dimensions of the frame
84 cm2 is the area of the frame
Call the width w
divide the top bottom and 2 sides into strips
{{{20w + 20w + (12-2w)*w + (12-2w)*w = 84}}}
{{{40w + 2w*(12-2w) = 84}}}
{{{40w + 24w - 4w^2 = 84}}}
rearranging
{{{4w^2 - 64w + 84 = 0}}}
divide both sides by 4
{{{w^2 - 16w + 21 = 0}}}
{{{w = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
where {{{a = 1}}}, {{{b = -16}}}, {{{c = 21}}}
{{{w = (16 +- sqrt( (-16)^2-4*1*21 ))/(2*1) }}}
{{{w = (16 +- sqrt(256-84 ))/2 }}}
{{{w = (16 +- sqrt(172))/2 }}}
{{{w = (16 + 13.11) / 2}}} and
{{{w = (16 - 13.11) / 2}}}
The 1st answer doesn't make sense, so pick the 2nd
{{{w = 2.89/2}}}
{{{w = 1.44}}}cm answer