Question 1051152
Let {{{ A }}} = the original area
{{{ A = 8*12 }}}
{{{ A = 96 }}}
{{{ 2A = 192 }}}
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{{{ ( 8 + x )*( 12 + x ) = 192 }}}
{{{ 96 + 12x + 8x + x^2  = 192 }}}
{{{ x^2 + 20x = 96 }}}
Complete the square
{{{ x^2 + 20x + ( 20/2 )^2 = 96 + ( 20/2 )^2 }}}
{{{ x^2 + 20x + 100 =  196 }}}
{{{ ( x + 10 )^2 = 14^2 }}}
{{{ x + 10 = 14 }}}
{{{ x = 4 }}}
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{{{ 8 + x = 12 }}}
{{{ 12 + x = 16 }}}
The new dimensions are 12 x 16
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check:
{{{ 8*12 = 96 }}}
and
{{{ 12*16 = 192 }}}
{{{ 2*96 = 192 }}}
OK