Question 736721
The area of the picture plus the frame is
{{{ 18*14 = 252 }}} in2
{{{ 252 - 221 = 31 }}} in2
If {{{ x }}} = the width of the frame,
{{{ A = 18x + 18x + ( 14 - 2x )*x + ( 14 - 2x )*x }}}
{{{ A = 36x + 2x*( 14 - 2x ) }}}
{{{ A = -4x^2 + 28x + 36x }}}
{{{ A = -4x^2 + 64x }}}
{{{ -4x^2 + 64x - 31 = 0 }}}
Use quadratic formula
{{{ x = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}} 
{{{ a = -4 }}}
{{{ b = 64 }}}
{{{ c = -31 }}}
{{{ x = (-64 +- sqrt( 64^2 - 4*(-4)*(-31) )) / (2*(-4)) }}} 
{{{ x = (-64 +- sqrt( 4096 - 496 )) / (-8) }}} 
{{{ x = (-64 +- sqrt( 3600 )) / (-8) }}} 
{{{ x = ( -64 + 60 ) / (-8) }}}
{{{ x = 1/2 }}}
and, the other answer is:
{{{ x = ( -64 - 60 ) / (-8) }}}
{{{ x = 15.5 }}} ( impossible for width of frame )
The width of the frame is 1/2 in
check:
{{{ A = 36x + 2x*( 14 - 2x ) }}}
{{{ A = 36*(1/2) + 2*(1/2)*( 14 - 2*(1/2) ) }}}
{{{ A = 18 + 1*( 13 ) }}}
{{{ A = 31 }}}
OK