three parallel lines

three parallel lines

an equilateral triangle has a corner on each of the parallel lines
the (perpendicular) distances between the parallel lines are shown
what is the length of the side of the equilateral triangle?

mega-hard questions (but only involving pythagoras - to set up three equations)
integer answers to these questions
but not generally.... 

if students are told that there are integer solutions they can use trial and improvement, in three equations

maybe there is an easier way to do it ....(?)