Question 927524
given:
the base of a triangle {{{a}}} is {{{3cm}}} longer than it's corresponding height {{{h}}} 
the area is {{{44cm^2}}}

{{{A=a*h/2}}}

if  {{{a=h+3cm}}}, then

{{{44cm=(h+3cm)*h/2}}}

{{{44cm^2*2=h^2+3hcm}}}

{{{88cm^2=h^2+3hcm}}}

{{{0=h^2+3hcm-88cm^2}}}


{{{h = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


{{{h = (-3cm +- sqrt( (3cm)^2-4*1*(-88cm^2) ))/(2*1) }}} 


{{{h = (-3cm +- sqrt( 9cm^2+352cm^2) )/2 }}}


{{{h = (-3cm +- sqrt( 361cm^2) )/2 }}}


{{{h = (-3cm +- 19cm )/2 }}}...we need only positive solution


{{{h = (-3cm + 19cm )/2 }}}


{{{h = 16cm /2 }}}


{{{highlight(h = 8cm)  }}}


now, find the base:


{{{a=h+3cm}}}


{{{a=16cm+3cm}}}


{{{highlight(a=19cm)}}}=> the length of it's base