Question 825679
Let {{{ w }}} = the width of the matte in cm
On one side, the matte plus print =
{{{ 50 + 2w }}} cm
On the other side:
{{{ 75 + 2w }}}
-------------
The area of matte plus print is:
{{{ A = ( 50 + 2w )*( 75 + 2w ) }}}
{{{ A = 3750 + 150w + 100w + 4w^2 }}} cm2
This area minus the area of the print plus 
the area of the matte which also equals 
the area of the print
{{{ 3750 + 150w + 100w + 4w^2 = 2*50*75 }}}
{{{ 3750 + 150w + 100w + 4w^2 = 7500 }}} cm2
{{{ 4w^2 + 250w - 3750 = 0 }}}
{{{ 2w^2 + 125w - 1875 = 0 }}}
{{{ w = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 2 }}}
{{{ b = 125 }}}
{{{ c = -1875 }}}
{{{ w = ( -125 +- sqrt( 125^2 - 4*2*(-1875) )) / (2*2) }}}
{{{ w = ( -125 +- sqrt( 15625 + 15000 )) / 4 }}} 
{{{ w = ( -125 +- sqrt( 30625 )) / 4 }}} 
{{{ w = ( -125 + 175) / 4 }}} ( I can't use the (-) square root )
{{{ w = 50/4 }}}
{{{ w = 12.5 }}} cm
----------------
check:
{{{ 50*75 = 3750 }}} cm2
The area of matte plus print is:
{{{ A = ( 50 + 2w )*( 75 + 2w ) }}}
{{{ A = ( 50 + 2*12.5 )*( 75 + 2*12.5 ) }}}
{{{ A = ( 50 + 25 )*( 75 + 25 ) }}}
{{{ A = 75*100 }}}
{{{ A = 7500 }}} cm2
{{{ A/2 = 7500/2 }}}
{{{ A/2 = 3750 }}} cm
The area of the matte or the print