Question 1133131
Call the larger triangle ABC
Then the smaller triangle CDE is similar to ABC (all angles are equal, AAA).

AB is the side that is 36, and we wish to find DE, the side corresponding to AB<br>

Area_CDE = Area_ABC - Area_CDE  -->  Area_ABC / Area_CDE = 2<br>

Let x=length of DE
Ratio of areas = (ratio of sides)^2
  {{{ 2 = (36/x)^2 }}}
  {{{ 2 = 1296/x^2 }}}
  {{{  x^2 = 1296/2 = 648 }}}
   {{{ x = sqrt(648) }}} or approx. {{{ highlight( 25.45584 ) }}}