Question 863010
Let {{{ w }}} = the width
{{{ 2w - 9 }}} = the length
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The area = ( length ) x ( width )
{{{ A = ( 2w - 9 )*w }}}
{{{ 11 = ( 2w - 9 )*w }}}
{{{ 2w^2 - 9w = 11 }}}
{{{ 2w^2 - 9w - 11 = 0 }}}
Use the quadratic formula
{{{ w = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 2 }}}
{{{ b = -9 }}}
{{{ c = -11 }}}
{{{ w = ( -(-9) +- sqrt( (-9)^2 - 4*2*(-11) )) / (2*2) }}}
{{{ w = ( 9 +- sqrt( 81 + 88 )) / 4 }}}
{{{ w = ( 9 +- sqrt( 169 )) / 4 }}}
{{{ w = ( 9 + 13 ) / 4 }}}
{{{ w = 11/2 }}}
and
{{{ 2w - 9 = 2*(11/2) - 9 }}}
{{{ 2w - 9 = 11 - 9 }}}
{{{ 2w - 9 = 2 }}}
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The dimensions are:
5.5 cm x 2 cm
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check:
{{{ A = ( 2w - 9 )*w }}}
{{{ A = 2*5.5 }}}
{{{ A = 11 }}} cm2 
OK