Question 669064
What they are saying is that you need to end
up with a piece of plasterboard that is 
4 feet by {{{ l }}} feet, and you need the formula
{{{ l^2 = w*( l + w ) }}} to find {{{ l }}}
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{{{  w = 4 }}}
{{{ l^2 = 4*( l + 4 ) }}}
{{{ l^2 = 4l + 16 }}}
{{{ l^2 - 4l = 16 }}}
Complete the square
{{{ l^2 - 4l + ( (-4)/2 )^2 = ( (-4)/2 )^2 + 16 }}}
{{{ l^2 - 4l + 4 = 4 + 16 }}}
{{{ ( l - 2 )^2 = ( sqrt(20) )^2 }}}
{{{ i - 2 = sqrt(20) }}}
{{{ l = 2 + 2*sqrt(5) }}}
{{{ l = 2 + 4.472 }}}
{{{ l = 6.472 }}}
The dimensions are 4' x 6.472'
check:
{{{ l^2 = 4*( l + 4 ) }}}
{{{ 41.887 = 4*10.472 }}}
{{{ 41.887 = 41.888 }}}
Looks close enough