Question 1059648
Let {{{ x }}} = the thickness of the frame
{{{ ( 14 - 2x )*( 20 - 2x ) = 172 }}}
{{{ 280 - 40x - 28x + 4x^2 = 172 }}}
{{{ 4x^2 - 68x + 280 = 172 }}}
{{{ 4x^2 - 68x + 108 = 0 }}}
{{{x^2 - 17x + 27 = 0 }}}
{{{ x = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 1 }}}
{{{ b = -17 }}}
{{{ c = 27 }}}
{{{ x = ( -(-17) +- sqrt( (-17)^2 - 4*1*27 )) / (2*1) }}}
{{{ x = ( 17 +- sqrt( 289 - 108 )) / 2 }}}
{{{ x = ( 17 +- sqrt( 181 )) / 2 }}}
{{{ x = ( 17 - 13.4536 ) / 2 }}} ( note the + sqrt gives too big a number )
{{{ x = 3.5464 / 2 }}}
{{{ x = 1.7732 }}}
The thickness of the frame is 1.7732 in.
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check:
{{{ ( 14 - 2x )*( 20 - 2x ) = 172 }}}
{{{ ( 14 - 2*1.7732 )*( 20 - 2*1.7732 ) = 172 }}}
{{{ ( 14 - 3.5464 )*( 20 - 3.5464 ) = 172 }}}
{{{ 10.4536*16.4536 = 172 }}}
{{{ 171.9993 = 172 }}}
close enough