Question 181568
Call the legs {{{a}}} and {{{b}}} and the
hypotenuse {{{c}}}
given:
{{{h + b + c = 18}}}
{{{c = 8}}}
so,
{{{h + b + 8 = 18}}}
{{{h + b = 10}}}
{{{b = 10 - h}}}
Now I can say the sides are
{{{h}}}, {{{b = 10 - h}}}, and {{{c = 8}}}
The pythagorean theorem is
{{{h^2 + (10 - h)^2  = 8^2}}}
{{{h^2 + 100 - 20h + h^2 = 64}}}
{{{2h^2 - 20h + 36 = 0}}}
{{{h^2 - 10h + 18 = 0}}}
{{{h = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 1}}}
{{{b = -10}}}
{{{c = 18}}}
{{{h = (-(-10) +- sqrt( (-10)^2-4*1*18 ))/(2*1) }}}
{{{h = (10 +- sqrt(100 - 72))/2 }}}
{{{h = (10 +- sqrt(100 - 72))/2 }}}
{{{h = (10 + sqrt(28)) / 2}}}
{{{h = (10 + 5.29)/2}}}
{{{h = 7.65}}}
and
{{{h = (10 - sqrt(28)) / 2}}}
{{{h = (10 - 5.29) / 2}}}
{{{h = 2.35}}}
These 2 values for {{{h}}} turn out to be the legs of the 
right triangle, since
{{{h + b = 10}}}
{{{7.65 + 2.35 = 10}}}
and
{{{h^2 + b^2  = 8^2}}}
{{{7.65^2 + 2.35^2 = 64}}}
{{{58.52 + 5.52 = 64}}}
{{{64 = 64}}}
The area is:
{{{A = (1/2)*b*h}}}
{{{A = (1/2)*2.35*7.65}}}
{{{A = 8.99}}} answer