Question 1012352
Put this on a graph with the 8' wall on
the y-axis.
( 0,8 ) is the inside height of short wall
( x[1], 12 ) is the middle of the inside roof
( 2x[1], y[1] ) is the inside height of highest wall
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Equation for the ceiling line would be:
{{{ y = m*x + b }}}
{{{ b = 8 }}} ( y-intercept )
{{{ m = 1/3 }}} ( slope )
{{{ y = (1/3)*x + 8 }}}
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Plug in ( x[1], 12 )
{{{ y = (1/3)*x + 8 }}}
{{{ 12 = (1/3)*x[1] + 8 }}}
{{{ 12 - 8 = (1/3)*x[1] }}}
{{{ (1/3)*x[1] = 4 }}}
{{{ x[1] = 12 }}}
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Plug in 
( 2x[1], y[1] )
{{{ y = (1/3)*x + 8 }}}
{{{ y[1] = (1/3)*2x[1] + 8 }}}
{{{ y[1] = (1/3)*2*12 + 8 }}}
{{{ y[1] = 8 + 8 }}}
{{{ y[1] = 16 }}} ( this was an extra step )
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{{{ 2x[1] = 24 }}}
The width of the cabin is 24'
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Here's a plot of this ceiling line:
{{{ graph( 700,500, -4, 28, -4, 20, (1/3)*x + 8 ) }}}