Question 744774
The length of the bases may be m and 2m.  If you draw a trapezoid with one leg making right angles with each base, then this leg is also a height.


Area {{{336=16*(m+2m)/2}}}
{{{16*3m/2=336}}}
{{{8*3m=336}}}
{{{m=336/24}}}
{{{m=14}}} and then {{{2m=28}}}


Now if you have drawn this, the other leg is the hypotenuse of a right triangle.  The base of this triangle may be seen as m and the height is again 16.  The hypotenuse can be found.  h is hypotenuse, this other leg, {{{h^2=14^2+16^2}}}.


The perimeter of the trapezoid is {{{ m + 2m + 16 + h = 3*14+16+h}}}



-----------------------
{{{h=2sqrt(113)}}}, so perimeter is {{{58+2*sqrt(113)}}}