Question 1056747
I'll assume a uniform thickness all around
{{{ ( 14 - 2x )*( 19 - 2x ) = 150 }}}
{{{ 266 - 38x - 28x + 4x^2 = 150 }}}
{{{ 4x^2 - 66x + 116 = 0 }}}
{{{ 2x^2 - 33x + 58 = 0  }}}
Use the quadratic formula
{{{ x = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 2 }}}
{{{ b = -33 }}}
{{{ c = 58 }}}
{{{ x = ( -(-33) +- sqrt( (-33)^2 - 4*2*58 )) / (2*2) }}}
{{{ x = ( 33 +- sqrt( 1089 - 464 )) / 4 }}}
{{{ x = ( 33 +- sqrt( 625 )) / 4 }}}
{{{ x = ( 33 - 25 ) / 4 }}} ( using the positive square root gives an impossible answer )
{{{ x = 8/4 }}}
{{{ x = 2 }}}
The thickness of the frame is 2 inches
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check:
{{{ ( 14 - 2x )*( 19 - 2x ) = 150 }}}
{{{ ( 14 - 2*2 )*( 19 - 2*2 ) = 150 }}}
{{{ ( 14 - 4 )*( 19 - 4 ) = 150 }}}
{{{ 10*15 = 150 }}}
{{{ 150 = 150 }}}
OK