Question 318542
Let {{{b}}} = the base 
Let {{{h}}} = the height
{{{A = (1/2)*b*h}}}
given:
{{{b = h + 6}}} cm
{{{A = 36}}} cm2
---------------
{{{36 = (1/2)*b*h}}}
{{{36 = (1/2)*(h + 6)*h}}}
{{{36 = (1/2)*(h^2 + 6h)}}}
Multiply both sides by {{{2}}}
{{{72 = h^2 + 6h}}}
{{{h^2 + 6h - 72 = 0}}}
Use quadratic formula
 {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 1}}}
{{{b = 6}}}
{{{c = -72}}}
 {{{h = (-6 +- sqrt( 6^2-4*1*(-72) ))/(2*1) }}}
 {{{h = (-6 +- sqrt( 36 + 288 ))/2 }}}
 {{{h = (-6 +- sqrt( 324 ))/2 }}}
{{{h = (-6 + 18)/2}}} (can't use the negative square root)
{{{h = 12/2}}}
{{{h = 6}}}
and, since
{{{b = h + 6}}}
{{{b = 12}}}
The height is 6 cm and the base is 12 cm
check:
{{{A = (1/2)*12*6}}}
{{{A = (1/2)*72}}}
{{{A = 36}}} cm2
OK