Question 737218
Let {{{ x }}} = the width in cm of the original window
{{{ x + 2 }}} = the length in cm  of the original window 
The area of the original window is
{{{ A = x*( x + 2 ) }}}
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The widow with increased area is:
{{{ A + 72 = 2x*(2*( x + 2 )) }}}
{{{ A = 2x*(2*( x + 2 ))  - 72 }}}
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By substitution:
{{{ x( x+2 ) = 2x*(2*( x + 2 ))  - 72 }}}
{{{ x^2 + 2x = 2x*( 2x + 4 ) - 72 }}}
{{{ x^2 + 2x = 4x^2 + 8x - 72 }}}
{{{ 3x^2 + 6x -72 = 0 }}}
{{{ x^2 + 2x - 24 = 0 }}}
{{{ ( x + 6 )*( x - 4 ) = 0 }}} ( by inspection )
{{{ x = 4 }}} ( reject the other solution - can't be negative )
{{{ x + 2 = 6 }}}
The original rectangle is 4 x 6 cm2
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check:
If both the length and width are doubled,
it is 8 x 12 cm2
{{{ A[1] = 4*6 }}}
{{{ A[1] = 24 }}} cm2
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{{{ A[2]= 8*12 }}}
{{{ A[2] = 96 }}} cm2
{{{ A[2] - A[1] = 96 - 24 }}}
{{{ A[2] - A[1] = 72 }}}
OK