Question 1034780
Call the sides:
{{{ a = 8 }}}
{{{ b = 15 }}}
{{{ c = 20 }}}
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Call {{{ h }}} the perpendicular from
the junction of {{{ a }}} and {{{ b }}}
to side {{{ c }}}
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{{{ h }}} divides {{{ c }}} into
{{{ x }}} and {{{ c - x }}}
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{{{ h^2 = a^2 - x^2 }}}
and
{{{ h^2 = b^2 - ( c - x )^2 }}}
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{{{ a^2 - x^2 = b^2 - ( c - x )^2 }}}
Plug in the numbers
{{{ 8^2 - x^2 = 15^2 - ( 20 - x )^2 }}}
{{{ 64 - x^2 = 225 - ( 400 - 40x + x^2 ) }}}
{{{ 64 - x^2 = 225 - 400 + 40x - x^2 ) }}}
{{{ 64 = -175 + 40x }}}
{{{ 40x = 239 }}}
{{{ x = 5.975 }}}
and
{{{ h^2 = a^2 - x^2 }}}
{{{ h^2 = 8^2 - 5.975^2 }}}
{{{ h^2 = 64 - 35.7 }}}
{{{ h^2 = 28.3 }}}
{{{ h = 5.32 }}}
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Let area  = {{{ A }}}
{{{ A = (1/2)*c*h }}}
{{{ A = (1/2)*20*5.32 }}}
{{{ A = 53.2 }}}
The area is 53.2 ft2
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Definitely get another opinion on this
if you can -I could easily have messed up
the calculations