Question 16701
let x = the height any y = the base.
We know that x = y - 8 and {{{1/2 * x * y}}}= 192
Pluggin the x = y - 8 into the second equation yields
{{{(1/2) * (y-8) * y}}} = 192
or 
{{{(1/2) * y^2 - 4 * y}}} = 192
and
{{{(1/2)y^2 - 4y - 192}}} = 0
then use the quadratic equation to solve for y
{{{(4 +- sqrt((-4)^2 - 4 * (1/2) * -192))/(2 * (1/2))}}}

y = 4 + 20 or y = 4 - 20.  Since we are dealing with length then a negative value doesn't make sense so y = 4 + 20 = 24.
Now use y to solve for x. 
x = y - 8 = 24 - 8 = 16.
So x = 16 = the height 
and
y = 24 = the base
Check: 16 * 24 = 384
384 / 2 = 192