Question 890279
{{{ 14*20 = 280 }}} in2 of total area
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The width is uniform all around, I assume
Let {{{ x }}} = the width of the frame
{{{ ( 14 - 2x )*( 20 - 2x ) = 160 }}}
{{{ 280 - 40x - 28x + 4x^2 = 160 }}}
{{{ 4x^2 - 68x + 120 = 0 }}}
{{{ x^2 - 17x + 30 = 0 }}}
Use quadratic formula to solve:
{{{x = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}} 
{{{ a = 1 }}}
{{{ b = -17 }}}
{{{ c = 30 }}}
{{{x = ( -(-17) +- sqrt( (-17)^2 - 4*1*30 )) / (2*1) }}} 
{{{x = ( 17 +- sqrt( 289 - 120 )) / 2 }}} 
{{{x = ( 17 +- sqrt( 169 )) / 2 }}} 
{{{ x = ( 17 - 13 ) / 2 }}}
{{{ x = 4/2 }}}
{{{ x = 2 }}}
Note that I used the negative square root of {{{ 169 }}}
because if I used the positive square root, I would
get {{{ x = 15 }}}, which makes no sense
So, the width of the frame is 2 inches
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check:
{{{ ( 14 - 2x )*( 20 - 2x ) = 160 }}}
{{{ ( 14 - 2*2 )*( 20 - 2*2 ) = 160 }}}
{{{ 10*16 = 160 }}}
OK